Authors
Tag |
Content |
Author |
Aref'eva, I.Ya and Bulatov, N.V. and Joukovskaya, L.V. and Vernov, S.Yu. |
Title |
Null energy condition violation and classical stability in the Bianchi I metric |
Year |
2009 |
Address |
United States |
Annote |
The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for a positive Hubble parameter follows from their stability in the Friedmann-Robertson-Walker metric. This result is applied to models inspired by string field theory, which violate the null energy condition. Examples of stable isotropic solutions are presented. We also consider the k-essence model and analyze the stability of solutions of the form Phi(t) = t. |
Doi |
10.1103/PhysRevD.80.083532 |
Issn |
0556-2821; 1550-7998 |
Journal |
Physical Review D - Particles, Fields, Gravitation and Cosmology |
Language |
english |
Number |
8 |
Pages |
083532 |
Publisher |
United States |
Volume |
80 |
Tag |
Content |
Author |
Aref'eva, I.Ya and Bulatov, N.V. and Vernov, S.Yu. |
Title |
Stable exact solutions in cosmological models with two scalar fields |
Year |
2010 |
Address |
Russian Federation |
Annote |
We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory. |
Doi |
10.1007/s11232-010-0063-x |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
3 |
Pages |
788--803 |
Publisher |
Russian Federation |
Volume |
163 |
Tag |
Content |
Author |
Aref'eva, I.Ya and Koshelev, A.S. and Vernov, S.Yu. |
Title |
Stringy dark energy model with cold dark matter |
Year |
2005 |
Address |
Netherlands |
Annote |
Cosmological consequences of adding the cold dark matter (CDM) to the exactly solvable stringy dark energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the string field theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial value of the CDM energy density are found. Solutions with large initial value of the CDM energy density attracted by the exact solution without CDM are constructed numerically. In contrast to the ACDM model the Hubble parameter in the model is not a monotonic function of time. For specific initial data the DE state parameter w(DE) is also not monotonic function of time. For these cases there are two separate regions of time where wDE being less than -1 is close to -1. (c) 2005 Elsevier B.V. All fights reserved. |
Doi |
0.1016/j.physletb.2005.09.017 |
Issn |
0370-2693 |
Journal |
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
Language |
english |
Number |
1-2 |
Pages |
1--10 |
Publisher |
Netherlands |
Volume |
628 |
Tag |
Content |
Author |
Aref'eva, I.Ya and Koshelev, A.S. and Vernov, S.Yu. |
Title |
String field theory inspired phantom model |
Year |
2006 |
Booktitle |
Proc. of Third Advanced Research Workshop \"Gravity, Astrophysics and Strings at the Black Sea\" |
Language |
english |
Pages |
10--21 |
Publisher |
St. Kliment Ohridski University Press Sofia, Bulgaria |
Tag |
Content |
Author |
Aref'eva, I.Ya and Koshelev, A.S. and Vernov, S.Yu. |
Title |
Exact Solutions in w<в€’1 SFT Inspired Cosmological Models |
Year |
2006 |
Annote |
Exact solutions to the Friedmann equations with a stringy inspired phantom field are constructed. The Universe is considered as a slowly decaying D3-brane, which is described in the string field theory (SFT) framework. The D3-brane dynamics is approximately described by a nonlocal string tachyon interaction and the back reaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this model contains one phantom component and one usual scalar field. The notable feature of this model is a ghost sign of the kinetic term of the phantom scalar field. We find explicit solutions with the Dark Energy state parameter wDE reaching the barrier w_DE=-1 from below at large time. |
Journal |
Bulgarian Journal of Physics |
Language |
english |
Number |
S1 |
Pages |
360--367 |
Volume |
33 |
Tag |
Content |
Author |
Aref'eva, I.Ya and Koshelev, A.S. and Vernov, S.Yu. |
Title |
Crossing the w=-1 barrier in the D3-brane dark energy model |
Year |
2005 |
Address |
United States |
Annote |
We explore a possibility for the Universe to cross the w=-1 cosmological constant barrier for the dark energy state parameter. We consider the Universe as a slowly decaying D3-brane. The D3-brane dynamics are approximately described by a nonlocal string tachyon interaction and the backreaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this model contains one phantom component and one usual field with a simple polynomial interaction. To understand cosmological properties of this system we study toy models with the same scalar fields but with modified interactions. These modifications admit polynomial superpotentials. We find restrictions on these interactions under which it is possible to reach w=-1 from below at large time. Explicit solutions with the dark energy state parameter crossing or not crossing the barrier w=-1 at large time are presented. |
Doi |
10.1103/PhysRevD.72.064017 |
Issn |
0556-2821; 1550-7998 |
Journal |
Physical Review D - Particles, Fields, Gravitation and Cosmology |
Language |
english |
Number |
6 |
Pages |
064017 |
Publisher |
United States |
Volume |
72 |
Tag |
Content |
Author |
Aref'eva, I.Ya and Vernov, S.Yu and Koshelev, A.S. |
Title |
Exact solution in a string cosmological model |
Year |
2006 |
Address |
Russian Federation |
Annote |
We construct an exact solution of the Friedmann equations with a phantom scalar matter field originating in string field theory and show the absence of the big-rip singularity. The notable features of the model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable under small fluctuations of the initial conditions and special variations of the form of the potential. |
Doi |
10.1007/s11232-006-0086-5 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
1 |
Pages |
895--909 |
Publisher |
Russian Federation |
Volume |
148 |
Tag |
Content |
Author |
Aref'eva, Irina Ya and Bulatov, Nikolay V. and Gorbachev, Roman V. and Vernov, Sergey Yu. |
Title |
Non-minimally coupled cosmological models with the Higgs-like potentials and negative cosmological constant |
Year |
2014 |
Address |
United Kingdom |
Annote |
We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models, the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions, the Hubble parameter can perform either one or several cycles before becoming negative forever. |
Doi |
10.1088/0264-9381/31/6/065007 |
Issn |
0264-9381 |
Journal |
Classical and Quantum Gravity |
Language |
english |
Number |
6 |
Pages |
065007 |
Publisher |
United Kingdom |
Volume |
31 |
Tag |
Content |
Author |
Aref'eva, Irina Ya and Joukovskaya, Liudmila V. and Vernov, Sergey Yu. |
Title |
Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric |
Year |
2008 |
Address |
United Kingdom |
Annote |
A general class of cosmological models driven by a nonlocal scalar field inspired by string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing universe with the phantom dark energy. |
Doi |
10.1088/1751-8113/41/30/304003 |
Issn |
1751-8113; 1751-8121 |
Journal |
Journal of Physics A: Mathematical and Theoretical |
Language |
english |
Number |
30 |
Pages |
304003 |
Publisher |
United Kingdom |
Volume |
41 |
Tag |
Content |
Author |
Aref'eva, Irina Ya and Joukovskaya, Liudmila V. and Vernov, Sergey Yu. |
Title |
Bouncing and accelerating solutions in nonlocal stringy models |
Year |
2007 |
Address |
United Kingdom |
Annote |
A general class of cosmological models driven by a nonlocal scalar field inspired by string field theories is studied. In particular cases the scalar field is a string dilaton or a string tachyon. A distinguished feature of these models is a crossing of the phantom divide. We reveal the nature of this phenomena showing that it is caused by an equivalence of the initial nonlocal model to a model with an infinite number of local fields some of which are ghosts. Deformations of the model that admit exact solutions are constructed. These deformations contain locking potentials that stabilize solutions. Bouncing and accelerating solutions are presented. |
Doi |
10.1088/1126-6708/2007/07/087 |
Issn |
1029-8479; 1126-6708 |
Journal |
Journal of High Energy Physics |
Language |
english |
Number |
7 |
Pages |
087 |
Publisher |
United Kingdom |
Volume |
0707 |
Tag |
Content |
Author |
Biswas, T. and Koshelev, A.S. and Mazumdar, A. and Vernov, S.Yu. |
Title |
Stable bounce and inflation in non-local higher derivative cosmology |
Year |
2012 |
Address |
United Kingdom |
Annote |
One of the greatest problems of primordial inflation is that the inflationary space-time is past-incomplete. This is mainly because Einstein's GR suffers from a space-like Big Bang singularity. It has recently been shown that ghost-free, non-local higher-derivative ultra-violet modifications of Einstein's gravity may be able to resolve the cosmological Big Bang singularity via a non-singular bounce. Within the framework of such non-local cosmological models, we are going to study both sub- and super-Hubble perturbations around an inflationary trajectory which is preceded by the Big Bounce in the past, and demonstrate that the inflationary trajectory has an ultra-violet completion and that perturbations do not suffer from any pathologies. |
Doi |
10.1088/1475-7516/2012/08/024 |
Issn |
1475-7516 |
Journal |
Journal of Cosmology and Astroparticle Physics |
Language |
english |
Number |
08 |
Pages |
024 |
Publisher |
United Kingdom |
Volume |
2012 |
Tag |
Content |
Author |
Bulatov, Nikolay V. and Vernov, Sergey Yu. |
Title |
Stable cosmological solutions and superpotential method in two-field models |
Year |
2010 |
Annote |
The stability of isotropic cosmological solutions for two-field models in the Bianchi I metrics is considered. We have proved that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric are sufficient for the stability under anisotropic perturbations in the Bianchi I metric as well. The standard way to construct cosmological models with exact solutions in the Friedmann-Robertson-Walker metric is the superpotential method. We have used the superpotential method to construct stable kink-type solutions and obtained conditions on superpotential, which are sufficient conditions for the Lyapunov stability. We analyze the stability of isotropic kink-type solutions for quintom models related to the string field theory. |
Booktitle |
Proc. of the XIXth International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP2010) |
Language |
english |
Pages |
075 |
Publisher |
the International School for Advanced Studies (SISSA) Trieste, Italy |
Series |
Proceedings of Science |
Tag |
Content |
Author |
Edneral, V.F. and Smolyakov, M.N. and Vernov, S.Yu. and Volobuev, I.P. |
Title |
On periodic solutions in five-dimensional gravity |
Year |
2003 |
Booktitle |
Proceedings of 17th International Workshop on High-Energy Physics and Quantum Field Theory (QFTHEP 2003) |
Language |
english |
Pages |
321--324 |
Publisher |
MSU |
Tag |
Content |
Author |
Elizalde, E. and Lopez-Revelles, A.J. and Odintsov, S.D. and Vernov, S.Yu. |
Title |
Cosmological Models with Yang–Mills Fields |
Year |
2013 |
Address |
Russian Federation |
Annote |
Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term. |
Doi |
10.1134/S1063778813080097 |
Issn |
1562-692X; 1063-7788 |
Journal |
Physics of Atomic Nuclei |
Language |
english |
Number |
8 |
Pages |
996--1003 |
Publisher |
Russian Federation |
Volume |
76 |
Tag |
Content |
Author |
Elizalde, E. and Pozdeeva, E.O. and Vernov, S.Yu. |
Title |
Stability of de Sitter Solutions in Non-local Cosmological Models |
Year |
2012 |
Annote |
A non-local gravity model, which includes a function f(в–Ў^{в€’1}R), where в–Ў is the d'Alembert operator, is considered. For the model with an exponential f(в–Ў^{в€’1}R) de Sitter solutions are explored, without any restrictions on the parameters. Using Hubble-normalized variables, the stability of the de Sitter solutions is investigated, with respect to perturbations in the Bianchi I metric, in the case of zero cosmological constant, and sufficient conditions for stability are obtained. |
Booktitle |
Proc. of the XXth International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP2011) |
Language |
english |
Pages |
PoS(QFTHEP2011) 038 |
Publisher |
the International School for Advanced Studies (SISSA) Trieste, Italy Trieste, Italy |
Series |
Proceedings of Science |
Tag |
Content |
Author |
Elizalde, E. and Pozdeeva, E.O. and Vernov, S.Yu. |
Title |
De Sitter Universe in Non-local Gravity |
Year |
2012 |
Address |
United States |
Annote |
A nonlocal gravity model, which does not assume the existence of a new dimensional parameter in the action and includes a function f(\Box R^{-1}), with square the d'Alembertian operator, is considered. The model is proven to have de Sitter solutions only if the function f satisfies a certain second-order linear differential equation. The de Sitter solutions corresponding to the simplest case, an exponential function f, are explored, without any restrictions on the parameters. If the value of the Hubble parameter is positive, the de Sitter solution is stable at late times, both for negative and for positive values of the cosmological constant. Also, the stability of the solutions with zero cosmological constant is discussed and sufficient conditions for it are established in this case. New de Sitter solutions are obtained, which correspond to the model with dark matter, and stability is proven in this situation for nonzero values of the cosmological constant. |
Doi |
10.1103/PhysRevD.85.044002 |
Issn |
0556-2821; 1550-7998 |
Journal |
Physical Review D - Particles, Fields, Gravitation and Cosmology |
Language |
english |
Number |
4 |
Pages |
044002 |
Publisher |
United States |
Volume |
85 |
Tag |
Content |
Author |
Elizalde, Emilio and Pozdeeva, Ekaterina O. and Vernov, Sergey Yu. |
Title |
Reconstruction procedure in nonlocal cosmological models |
Year |
2013 |
Address |
United Kingdom |
Annote |
A nonlocal gravity model is considered which does not assume the existence of a new dimensional parameter in the action and includes a function f (□ −1 R ), with □ the d’Alembertian operator. Using a reconstruction procedure for the local scalar-tensor formulation of this model, a function f is obtained for which the model exhibits power-law solutions with the Hubble parameter H = n / t , for any value of the constant n . For generic n —namely except for a few special values which are characterized and also specifically studied—the corresponding function f is a sum of exponential functions. Corresponding power-law solutions are found explicitly. Also the case is solved in all detail of a function f such that the model contains both de Sitter and power-law solutions. |
Doi |
doi:10.1088/0264-9381/30/3/035002 |
Issn |
0264-9381 |
Journal |
Classical and Quantum Gravity |
Language |
english |
Number |
3 |
Pages |
035002 |
Publisher |
United Kingdom |
Volume |
30 |
Tag |
Content |
Author |
Elizalde, Emilio and Pozdeeva, Ekaterina O. and Vernov, Sergey Yu. and Zhang, Ying-li |
Title |
Cosmological Solutions of a Nonlocal Model with a Perfect Fluid |
Year |
2013 |
Address |
United Kingdom |
Annote |
A nonlocal gravity model which does not assume the existence of a new dimensional parameter in the action and includes a function f(\Box^{в€’1}R), with \Box the d'Alembertian operator, is studied. By specifying an exponential form for the function f and including a matter sector with a constant equation of state parameter, all available power-law solutions in the Jordan frame are obtained. New power-law solutions in the Einstein frame are also probed. Furthermore, the relationship between power-law solutions in both frames, established through conformal transformation, is substantially clarified. The correspondence between power-law solutions in these two frames is proven to be a very useful tool in order to obtain new solutions in the Einstein frame. |
Doi |
10.1088/1475-7516/2013/07/034 |
Issn |
1475-7516 |
Journal |
Journal of Cosmology and Astroparticle Physics |
Language |
english |
Number |
07 |
Pages |
034 |
Publisher |
United Kingdom |
Volume |
2013 |
Tag |
Content |
Author |
Kamenshchik, A.Yu and Tronconi, A. and Venturi, G. and Vernov, S.Yu. |
Title |
Reconstruction of scalar potentials in modified gravity models |
Year |
2013 |
Address |
United States |
Annote |
We employ the superpotential technique for the reconstruction of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Robertson-Walker background. The key point in this method is that the Hubble parameter is considered as a function of the scalar field, and this allows one to reconstruct the scalar field potential and determine the dynamics of the field itself, without a priori fixing the Hubble parameter as a function of time or of the scale factor. The scalar field potentials that lead to de Sitter or asymptotic de Sitter solutions, and those that reproduce the cosmological evolution given by Einstein-Hilbert action plus a barotropic perfect fluid, have been obtained. |
Doi |
10.1103/PhysRevD.87.063503 |
Issn |
0556-2821; 1550-7998 |
Journal |
Physical Review D - Particles, Fields, Gravitation and Cosmology |
Language |
english |
Number |
6 |
Pages |
063503 |
Publisher |
United States |
Volume |
87 |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. |
Title |
Quantization close to periodic classical solutions (\phi^4 theory) |
Year |
1997 |
Booktitle |
Proceedings of XI International Workshop on High Energy Physics and Quantum Field Theory |
Language |
english |
Pages |
353--360 |
Series |
QFTHEP |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. |
Title |
Construction of doubly periodic solutions via the Poincare-Lindstedt method in the case of massless phi(4) theory |
Year |
2001 |
Address |
Netherlands |
Annote |
Doubly periodic (periodic both in time and in space) solutions for the Lagrange-Euler equation of the (1 + 1)-dimensional scalar phi (4) theory are studied. Provided that the nonlinear term is small, the Poincare-Lindstedt asymptotic method can be used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of Jacobi elliptic function. To obtain this leading-order term the system REDUCE is used. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved. |
Doi |
10.1016/S0378-4754(01)00342-1 |
Issn |
0378-4754 |
Journal |
Mathematics and Computers in Simulation |
Language |
english |
Number |
3-5 |
Pages |
239--252 |
Publisher |
Netherlands |
Volume |
57 |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. |
Title |
Construction of asymptotic periodic solutions for quasilinear wave equation in the case of massless \varphi^4 theory |
Year |
1999 |
Booktitle |
Proceedings of XII International Workshop on High Energy Physics and Quantum Field Theory |
Language |
english |
Pages |
408--414 |
Series |
QFTHEP |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. |
Title |
Approximate Standing Wave Solutions in Massless \varphi^4 Theory |
Year |
1999 |
Booktitle |
the Proceedings of the International Seminar \"Quarks-98\" (Suzdal, Russia, 1998) |
Language |
english |
Pages |
158--168 |
Volume |
2 |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. and Tchitchikina, M.V. |
Title |
Quantization in terms of Bogolyubov Group Variables |
Year |
2000 |
Booktitle |
Proceedings of XXII International Workshop on Fundamental Problems of High Energy Physics and Field Theory |
Language |
english |
Pages |
260--271 |
Publisher |
Institute for High Energy Physics Protvino, Russia |
Tag |
Content |
Author |
Khrustalev, O.A. and Vernov, S.Yu. and Tchitchikina, M.V. |
Title |
Bogolyubov Group Variables for Poincare-invariant Systems |
Year |
2000 |
Booktitle |
Proceedings of 15th International Workshop on High Energy Physics and Quantum Field Theory |
Language |
english |
Pages |
653--659 |
Publisher |
Moscow, Russia |
Tag |
Content |
Author |
Koshelev, A.S. and Vernov, S.Yu. |
Title |
On bouncing solutions in non-local gravity |
Year |
2012 |
Address |
Russian Federation |
Annote |
A non-local modified gravity model with an analytic function of the d'Alembert operator is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present an exact bouncing solution, which is simpler compared to the already known one in this model in the sense it does not require an additional matter to satisfy all the gravitational equations. |
Doi |
10.1134/S106377961205019X |
Issn |
1531-8559; 1063-7796 |
Journal |
Physics of Particles and Nuclei |
Language |
english |
Number |
5 |
Pages |
666--668 |
Publisher |
Russian Federation |
Volume |
43 |
Tag |
Content |
Author |
Koshelev, A.S. and Vernov, S.Yu. |
Title |
Cosmological perturbations in SFT inspired non-local scalar field models |
Year |
2012 |
Address |
Germany |
Annote |
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields. We also show that vector and tensor perturbations are absent in this set-up. |
Doi |
10.1140/epjc/s10052-012-2198-4 |
Issn |
1434-6044 |
Journal |
European Physical Journal C |
Language |
english |
Pages |
2198 |
Publisher |
Germany |
Volume |
72 |
Tag |
Content |
Author |
Koshelev, Alexey S. and Vernov, Sergey Yu. |
Title |
Analysis of scalar perturbations in cosmological models with a non-local scalar field |
Year |
2011 |
Address |
United Kingdom |
Annote |
We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex. |
Doi |
10.1088/0264-9381/28/8/085019 |
Issn |
0264-9381 |
Journal |
Classical and Quantum Gravity |
Language |
english |
Number |
8 |
Pages |
085019 |
Publisher |
United Kingdom |
Volume |
28 |
Tag |
Content |
Author |
Timoshkova, E.I. and Vernov, S.Yu. |
Title |
The Painleve analysis and construction of solutions for the generalized Henon-Heiles system |
Year |
2004 |
Annote |
The generalized Henon-Heiles system has been considered. In two nonintegrable cases new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. In these nonintegrable cases with the help of the Painleve test three-parameter special solutions have been found as Laurent series, converging in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the Laurent series solutions coincide with the Laurent series of the elliptic solutions, obtained in this paper. The Painleve test can be used not only to construct local solutions as the Laurent series, but also to find elliptic solutions. |
Booktitle |
Order and Chaos in Stellar and Planetary Systems |
Language |
english |
Pages |
28--33 |
Publisher |
ASTRONOMICAL SOC PACIFIC 390 ASHTON AVE, SAN FRANCISCO, CA 94112 USA |
Series |
ASTRONOMICAL SOCIETY OF THE PACIFIC CONFERENCE SERIES |
Volume |
316 |
Tag |
Content |
Author |
Timoshkova, E.I. and Vernov, S.Yu. |
Title |
The Painleve analysis and construction of solutions for the generalized Henon-Heiles system |
Year |
2004 |
Booktitle |
Proceedings of the XXVI-th International Workshop on the Fundamental Problems of High Energy Physics and Field Theory (Protvino, Russia, 2-4 July, 2003) |
Language |
english |
Pages |
133--142 |
Publisher |
РФВРПротвино, Р РѕСЃСЃРёСЏ |
Tag |
Content |
Author |
Timoshkova, E.I. and Vernov, S.Yu. |
Title |
New exact solutions for the generalized Henon-Heiles system |
Year |
2003 |
Booktitle |
Proceedings of 17th International Workshop on High-Energy Physics and Quantum Field Theory (QFTHEP 2003) |
Language |
english |
Pages |
450--457 |
Publisher |
MSU |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
The Painleve analysis and solutions with critical points |
Year |
2003 |
Booktitle |
Proceedings of 12th International Seminar on High-Energy Physics (QUARKS 2002) |
Language |
english |
Pages |
158--168 |
Publisher |
MSU |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
The Painleve Analysis and Asymptotic Solutions of the General Henon-Heiles System |
Year |
2002 |
Booktitle |
the Proceedings of the International School-Seminar \"Actual Problems of Particle Physics\" (7-16.08.2001) |
Language |
english |
Pages |
98--112 |
Volume |
2 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Solutions of nonlocal cosmological equations |
Year |
2010 |
Annote |
A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. The Ostrogradski representation for nonlocal gravitational models and the way of its localization are proposed. We study the action with an arbitrary analytic function F(square(g)), which has both simple and double roots. The way of localization allows to find solutions of nonlocal Einstein equations. |
Booktitle |
XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS |
Language |
english |
Pages |
185--190 |
Publisher |
AMER INST PHYSICS, MELVILLE, USA, NY, 11747-4501 |
Series |
AIP Conference Proceedings |
Volume |
1307 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Single-valued and multivalued solutions for the generalized Henon-Heiles system with an additional nonpolynomial term |
Year |
2005 |
Annote |
The generalized Hénon–Heiles system with an additional nonpolynomial term is considered. The standard method for the search of the elliptic solutions is a transformation of an initial nonlinear polynomial differential equation into a nonlinear algebraic system. It has been demonstrated that the use of the Laurent-series solutions allows to simplify the resulting algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial equation in the form of the Laurent or Puiseux series we use algorithm of the Painlevé test. |
Booktitle |
Proc. of International Conference on Geometry, Integrability and Quantization, (2-10 June, 2004, Varna, Bulgaria) |
Doi |
10.7546/giq-6-2005-297-309 |
Language |
english |
Pages |
297--309 |
Publisher |
SOFTEX Sofia, Bulgaria |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Reconstruction procedure in cosmological models with non-minimally coupled scalar fields |
Year |
2013 |
Booktitle |
GR20/Amaldi10 - Abstract Book |
Language |
english |
Pages |
49--49 |
Publisher |
University of Warsaw, Poland |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Proof of the absence of elliptic solutions of the cubic complex Ginzburg-Landau equation |
Year |
2006 |
Address |
Russian Federation |
Annote |
We consider the cubic complex Ginzburg-Landau equation. Using Hone's method, based on formal Laurent-series solutions and the residue theorem, we prove the absence of elliptic standing-wave solutions of this equation. This result complements a result by Hone, who proved the nonexistence of elliptic traveling-wave solutions. We show, that it is more efficient to apply Hone's method to a system of polynomial differential equations rather than to an equivalent differential equation. |
Doi |
10.1007/s11232-006-0013-9 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
1 |
Pages |
131--139 |
Publisher |
Russian Federation |
Volume |
146 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Painleve Analysis and Exact Solutions of Nonintegrable Systems |
Year |
2006 |
Annote |
Here we consider the cubic complex Ginzburg–Landau equation. Applying the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has no elliptic standing wave solutions. This result supplements Hone’s result, that this equation has no elliptic travelling wave solutions. It has been shown that the Hone’s method can be applied to a system of polynomial differential equations more effectively than to an equivalent differential equation. |
Booktitle |
Proc. of International Conference on Geometry, Integrability and Quantization, (2-10 June, 2005, Varna, Bulgaria) |
Doi |
10.7546/giq-7-2006-280-291 |
Language |
english |
Pages |
280--291 |
Publisher |
SOFTEX Sofia, Bulgaria |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Nonlocal gravitational models and exact solutions |
Year |
2012 |
Address |
Russian Federation |
Annote |
A nonlocal gravity model with a function f(\Box6-1 R), where \Box is the d'Alembert operator, is considered. The algorithm, allowing to reconstruct f, corresponding to the given Hubble parameter and the state parameter of the matter, is proposed. Using this algorithm, we find the functions f, corresponding to de Sitter solutions. |
Doi |
10.1134/S1063779612050371 |
Issn |
1531-8559; 1063-7796 |
Journal |
Physics of Particles and Nuclei |
Language |
english |
Number |
5 |
Pages |
694--696 |
Publisher |
Russian Federation |
Volume |
43 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Nonlocal cosmological models and exact solutions |
Year |
2010 |
Booktitle |
Proceedings of 16th International Seminar on High Energy Physics (QUARKS 2010) |
Language |
english |
Volume |
1 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions |
Year |
2011 |
Address |
Russian Federation |
Annote |
A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function в„±(в–Ў g), which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented. |
Doi |
10.1134/S1547477111030228 |
Issn |
1547-4771 |
Journal |
Physics of Particles and Nuclei Letters |
Language |
english |
Number |
3 |
Pages |
310--320 |
Publisher |
Russian Federation |
Volume |
8 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Interdependence between the Laurent-series and elliptic solutions of nonintegrable systems |
Year |
2005 |
Address |
HEIDELBERGER PLATZ 3, BERLIN, GERMANY,D-14197 |
Annote |
The standard methods for the search for the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and the search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent-series solutions of the initial differential equation assists to solve the obtained algebraic system and, thereby, simplifies the search for elliptic solutions. This procedure has been automatized with the help of the computer algebra systems Maple and REDUCE. The Laurent-series solutions also assist to solve the inverse problem: to prove the nonexistence of elliptic solutions. Using the Hone's method based on the use the Laurent-series solutions and the residue theorem, we have proved that the cubic complex one-dimensional Ginzburg-Landau equation has neither elliptic standing wave nor elliptic travelling wave solutions. To find solutions of the initial differential equation in the form of the Laurent series we use the Painleve test. |
Booktitle |
COMPUTER ALGEBRA IN SCIENFIFIC COMPUTING, PROCEEDINGS |
Language |
english |
Pages |
457--468 |
Publisher |
HEIDELBERGER PLATZ 3, BERLIN, GERMANY,D-14197 |
Series |
LECTURE NOTES IN COMPUTER SCIENCE |
Volume |
3718 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
From the Laurent-Series Solutions to Elliptic Solutions of Nonintegrable Systems |
Year |
2005 |
Booktitle |
Proc. of the International Seminar Quarks-2004 (23-30 May, 2004, Pushkinogorie, Russia) |
Language |
english |
Pages |
80--92 |
Volume |
2 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Exact solutions to nonlocal linear dark energy models |
Year |
2008 |
Annote |
A general class of cosmological models driven by a nonlocal scalar field is studied. We show that the considering linear cosmogical model with a nonlocal field can be transformed to models with local scalar fields. This transformation allows to find exact special solutions of the nonlocal Einstein equations. The exact solution in the Friedman-Robertson-Walker and Bianchi I metrics are presented. |
Booktitle |
Proc. of 5th Mathematical Physics Meeting: Summer School and Conference on Modern Mathematical Physics, MPHYS 2008 |
Language |
english |
Pages |
473--481 |
Publisher |
Inst. Phys. Belgrade, Serbia |
Series |
SFIN Ser. A: Conferences |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Exact and Asymptotic Solutions for the General Henon-Heiles System |
Year |
2002 |
Booktitle |
Proceedings of the International Workshop on Computer Algebra and its Application to Physics (CAAP-2001) |
Language |
english |
Pages |
337--347 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Exact Solutions in Nonlocal Linear Models |
Year |
2008 |
Booktitle |
Proc. of International Workshop \"Supersymmetry and Quantum Symmetries\" (July 30 - August 4, 2007, Dubna, Russia) |
Language |
english |
Pages |
118--121 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation |
Year |
2007 |
Address |
United Kingdom |
Annote |
The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a prior restriction is to simplify calculations by means of the use of a few Laurent-series solutions instead of one and the use of the residue theorem. The application of this approach to the quintic complex one-dimensional Ginzburg Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. Restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5, have been found as well. We demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation. |
Doi |
10.1088/1751-8113/40/32/009 |
Issn |
1751-8113; 1751-8121 |
Journal |
Journal of Physics A: Mathematical and Theoretical |
Language |
english |
Number |
32 |
Pages |
9833--9844 |
Publisher |
United Kingdom |
Volume |
40 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
EXACT SOLUTIONS OF NONLOCAL NONLINEAR FIELD EQUATIONS IN COSMOLOGY |
Year |
2011 |
Address |
Russian Federation |
Annote |
We consider a method for seeking exact solutions of the equation of a nonlocal scalar field in a nonflat metric. In the Friedmann-Robertson-Walker metric, the proposed method can be used in the case of an arbitrary potential except linear and quadratic potentials, and it allows obtaining solutions in quadratures depending on two arbitrary parameters. We find exact solutions for an arbitrary cubic potential, which consideration is motivated by string field theory, and also for exponential, logarithmic, and power potentials. We show that the k-essence field can be added to the model to obtain exact solutions satisfying all the Einstein equations. |
Doi |
10.1007/s11232-011-0031-0 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
3 |
Pages |
392--402 |
Publisher |
Russian Federation |
Volume |
166 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Crossing the cosmological constant barrier in string inspired models |
Year |
2007 |
Booktitle |
Proc. of 14th International Seminar on High Energy Physics \"QUARKS'2006\" |
Language |
english |
Pages |
341--353 |
Volume |
2 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of special solutions for nonintegrable systems with the help of the Painleve test |
Year |
2003 |
Booktitle |
Proceedings of the XXII-th International Workshop on the Fundamental Problems of High Energy Physics and Field Theory |
Language |
english |
Pages |
260--271 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of special solutions for nonintegrable systems |
Year |
2006 |
Address |
Sweden |
Annote |
The Painleve test is very useful to construct not only the Laurent series solutions of systems of nonlinear ordinary differential equations but also the elliptic and trigonometric ones. The standard methods for constructing the elliptic solutions consist of two independent steps: transformation of a nonlinear polynomial differential equation into a nonlinear algebraic system and a search for solutions of the obtained system. It has been demonstrated by the example of the generalized Henon-Heiles system that the use of the Laurent series solutions of the initial differential equation assists to solve the obtained algebraic system. This procedure has been automatized and generalized on some type of multivalued solutions. To find solutions of the initial differential equation in the form of the Laurent or Puiseux series we use the Painleve test. This test can also assist to solve the inverse problem: to find the form of a polynomial potential, which corresponds to the required type of solutions. We consider the five - dimensional gravitational model with a scalar field to demonstrate this. |
Doi |
10.2991/jnmp.2006.13.1.5 |
Issn |
1402-9251 |
Journal |
Journal of Nonlinear Mathematical Physics |
Language |
english |
Number |
1 |
Pages |
50--63 |
Publisher |
Sweden |
Volume |
13 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of solutions for nonintegrable systems with the help of the Painleve test |
Year |
2004 |
Address |
HEIDELBERGER PLATZ 3, BERLIN, GERMANY,D-14197 |
Annote |
The generalized Henon-Heiles system with an additional nonpolynomial term has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as converging Laurent series, depending on three parameters. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known elliptic solutions. The calculations have been made with use of computer algebra system REDUCE. The obtained local solutions can assist to find the elliptic three parameters solutions. The corresponding algorithm has been realized in REDUCE and Maple. |
Booktitle |
COMPUTATIONAL SCIENCE - ICCS 2004, PROCEEDINGS |
Language |
english |
Pages |
382--387 |
Publisher |
HEIDELBERGER PLATZ 3, BERLIN, GERMANY,D-14197 |
Series |
Lecture Notes in Computer Science |
Volume |
3039 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of singlevalued and multivalued solutions for nonintegrable systems |
Year |
2005 |
Booktitle |
Proceedings of the XVIIIth International Workshop on High Energy Physics and Quantum Field Theory |
Language |
english |
Pages |
369--375 |
Series |
QFTHEP |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series |
Year |
2006 |
Address |
United States |
Annote |
A package facilitating search for analytic solutions of nonintegrable systems of autonomous ordinary differential equations is suggested. The algorithm discussed, which is a generalization of the Conte-Musette method, allows one to obtain single-valued and multivalued analytical solutions that were known to exist only in the form of formal Laurent and Puiseux series (obtained, for example, by means of the Painleve analysis), respectively. Solutions in the form of the formal Laurent series and procedures from the package discussed are used not only for constructing elliptic solutions but also for proving impossibility of such construction. The suggested procedures have been implemented as packages in Maple and REDUCE. |
Doi |
10.1134/S0361768806020046 |
Issn |
1608-3261; 0361-7688 |
Journal |
Programming and Computer Software |
Language |
english |
Number |
2 |
Pages |
77--83 |
Publisher |
United States |
Volume |
32 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of asymptotic solutions for the generalized Henon-Heiles system in nonintegrable case |
Year |
2002 |
Booktitle |
Proceedings of XVI International Workshop on High Energy Physics and Quantum Field Theory |
Language |
english |
Pages |
406--413 |
Publisher |
Moscow University |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of Three-Parameter Solutions for the Generalized Hénon -Heiles System with the Help of the Painlevé Test |
Year |
2004 |
Annote |
The generalized Henon-Heiles system has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as Laurent series, depending on three parameters. The obtained series converge in some ring. One of parameters determines the singularity point location, other parameters determine coefficients of series. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known exact solutions. The Painleve test can be used not only to construct local solutions as the Laurent series but also to find elliptic solutions. |
Booktitle |
Mathematical Physics Frontiers |
Language |
english |
Publisher |
Nova Science Publishers, Inc NY, USA |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of Special Solutions for Nonintegrable Dynamical Systems with the help of the Painleve Analysis |
Year |
2004 |
Journal |
Proceedings of Institute of Mathematics of NAS of Ukraine |
Language |
english |
Number |
1 |
Pages |
504--512 |
Volume |
50 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test |
Year |
2004 |
Booktitle |
Proceedings of the International Conference \"Computer Algebra in Scientific Computing\" (CASC 2004, July 12-19, 2004, St. Petersburg, Russia) |
Language |
english |
Pages |
457--465 |
Publisher |
Technische Universitat Munchen, Germany Munchen, Germany |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Construction of Elliptic Solutions to the Quintic Complex One-Dimensional Ginzburg–Landau Equation |
Year |
2007 |
Annote |
The Conte-Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a priory restriction is to simplify calculations by means of the use of a few Laurent series solutions instead of one and the use of the residue theorem. The application of our approach to the quintic complex one-dimensional Ginzburg–Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. We also find restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions to the CGLE5. |
Booktitle |
Proc. of International Conference on Geometry, Integrability and Quantization (June 9–14, 2006, Varna, Bulgaria) |
Doi |
10.7546/giq-8-2007-322-333 |
Language |
english |
Pages |
322--333 |
Publisher |
SOFTEX Sofia, Bulgaria |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Constructing solutions for the generalized Henon-Heiles system through the Painleve test |
Year |
2003 |
Address |
Russian Federation |
Annote |
The generalized Henon-Heiles system is considered. New special solutions for two nonintegrable cases are obtained using the Painleve test. The solutions have the form of the Laurent series depending on three parameters. One parameter determines the singularity-point location, and the other two parameters determine the coefficients in the Laurent series. For certain values of these two parameters, the series becomes the Laurent series for the known exact solutions. It is established that such solutions do not exist in other nonintegrable cases. |
Doi |
10.1023/A:1024074702960 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
3 |
Pages |
792--801 |
Publisher |
Russian Federation |
Volume |
135 |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Chapter 15 - Gravitational Models with Nonlocal Scalar Fields |
Year |
2011 |
Annote |
Contemporary cosmological observation data strongly support that the present Universe exhibits an accelerated expansion providing thereby an evidence for a smoothly distributed dominating dark energy component with the state parameter close to minus one. The cosmological observations do not exclude an evolving dark energy state parameter. Moreover, the recent analysis of the observation data indicates that the varying in time dark energy with the state parameter, which crosses the cosmological constant barrier, gives a better fit than the cosmological constant. Cosmological models with scalar fields are the most popular alternative to models with the cosmological constant. A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function of the d'Alembert operator, which can has simple and double roots. The Ostrogradski representation for nonlocal gravitational models and the way of localization of nonlocal Einstein equations have been proposed for the general relativity models and generalized on the f(R) gravity models. The way of localization allows to find particular solutions of nonlocal equations of gravity. Exact solutions in the Friedmann-Robertson-Walker are presented. |
Booktitle |
Classical and Quantum Gravity: Theory, Analysis and Applications |
Language |
english |
Publisher |
Nova Science Publishers, Inc NY, USA |
Tag |
Content |
Author |
Vernov, S.Yu. |
Title |
Analysis of Scalar Perturbations in Nonlocal Cosmological Models |
Year |
2012 |
Booktitle |
Book of Abstracts of Ginzburg Conference on Physics |
Language |
english |
Pages |
151--152 |
Publisher |
Moscow |
Tag |
Content |
Author |
Vernov, S.Yu. and Chichikina, M.V. and Khrustalev, O.A. |
Title |
Quantization of relativistic-invariant systems in terms of Bogolyubov group variables. II. Construction of perturbation theory |
Year |
2004 |
Journal |
VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 3 FIZIKA ASTRONOMIYA |
Language |
english |
Number |
2 |
Pages |
6--10 |
Volume |
59 |
Tag |
Content |
Author |
Vernov, S.Yu. and Khrustalev, O.A. |
Title |
Approximate double-periodic solutions in (1+1)-dimensional rho(4)-theory |
Year |
1998 |
Address |
Russian Federation |
Annote |
Double-periodic solutions of the Euler-Lagrange equation for the (1 + 1)-dimensional scalar phi(4)-theory are considered. The nonlinear term is assumed to be small, and the Poincare method is used to seek asymptotic solutions in the standing-wave form. The principal resonance problem, which arises for zero mass, is resolved if the leading-order term is taken in the form of a Jacobi elliptic function. |
Doi |
10.1007/BF02557130 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
2 |
Pages |
881--889 |
Publisher |
Russian Federation |
Volume |
116 |
Tag |
Content |
Author |
Vernov, S.Yu. and Khurstalev, O.A. and Chichikina, M.V. |
Title |
Quantization of relativistic-invariant systems in terms of Bogolyubov group variables. I. Operators of coordinate and linear momentum |
Year |
2004 |
Journal |
Vestnik Moskovskogo Universita. Ser. 3 Fizika Astronomiya |
Language |
english |
Number |
1 |
Pages |
3--6 |
Volume |
59 |
Tag |
Content |
Author |
Vernov, S.Yu. and Timoshkova, E.I. |
Title |
On two nonintegrable cases of the generalized Henon-Heiles system |
Year |
2005 |
Address |
Russian Federation |
Annote |
The generalized Henon-Heiles system with an additional nonpolynoinial term is considered. In two nonintegrable cases, new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies searches for the elliptic solutions and allows them to be automatized. (c) 2005 Pleiades Publishing, Inc. |
Doi |
10.1134/1.2131124 |
Issn |
1562-692X; 1063-7788 |
Journal |
Physics of Atomic Nuclei |
Language |
english |
Number |
11 |
Pages |
1947--1955 |
Publisher |
Russian Federation |
Volume |
68 |
Tag |
Content |
Author |
Vernov, Sergey Yu. |
Title |
Reconstruction Procedure in Modified Gravity Cosmological Models |
Year |
2014 |
Annote |
We explorer reconstruction procedures for modified gravity cosmological models. The considering reconstruction procedures are proposed to reconstruct the potentials in cosmological models non-minimally coupled scalar fields and get models with suitable behaviour of the Hubble parameter and exact solutions. Such a method is similar to the Hamilton–Jacobi method (also known as the superpotential method or the first-order formalism) that applied to cosmological models with minimally coupled scalar fields. We show that this method is suitable for construction of induced gravity model with polynomial potentials. We also show that there are different algorithms of such reconstruction procedure for models with non-minimally coupled scalar fields. |
Booktitle |
Proc. of the XXIth International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP2013) |
Language |
english |
Pages |
PoS(QFTHEP2013)069 |
Publisher |
the International School for Advanced Studies (SISSA) Trieste, Italy |
Series |
Proceedings of Science |
Tag |
Content |
Author |
Vernov, Sergey Yu. |
Title |
Localization of nonlocal cosmological models with quadratic potentials in the case of double roots |
Year |
2010 |
Address |
United Kingdom |
Annote |
Nonlocal cosmological models with quadratic potentials are considered. We study the action with an arbitrary analytic function F(square(g)), which has both double and simple roots. The formulae for nonlocal energy-momentum tensors, which correspond to double roots, have been obtained. The way to find particular solutions for nonlocal Einstein equations in the case when F(square(g)) has both simple and double roots has been proposed. One and the same functions solve the initial nonlocal Einstein equations and the obtained local Einstein equations. |
Doi |
10.1088/0264-9381/27/3/035006 |
Issn |
0264-9381 |
Journal |
Classical and Quantum Gravity |
Language |
english |
Number |
3 |
Pages |
035006 |
Publisher |
United Kingdom |
Volume |
27 |
Tag |
Content |
Author |
Vernov, Sergey Yu. |
Title |
Gravitational models with non-local scalar fields |
Year |
2010 |
Annote |
A general class of f(R) gravity models with minimally coupling a nonlocal scalar field is considered. The Ostrogradski representation for nonlocal gravitational models with a quadratic potential and the way of its localization are proposed. We study the action with an arbitrary analytic function F(в–Ў), which has both simple and double roots. The way of localization allows to find particular solutions of nonlocal equations of gravity. |
Booktitle |
Proc. of the XIXth International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP2010) |
Language |
english |
Pages |
PoS(QFTHEP2010) 072 |
Publisher |
the International School for Advanced Studies (SISSA) Trieste, Italy |
Series |
Proceedings of Science |
Tag |
Content |
Author |
Vernov, Sergey Yu. |
Title |
Construction of exact solutions in two-fields models |
Year |
2009 |
Address |
Singapore |
Annote |
Dark energy model in the Friedmann Universe with a phantom scalar field, an usual scalar field and the polynomial potential has been considered. We demonstrate that the superpotential method is very effective to seek new solutions and to construct a two-parameter set of exact solutions to the Friedmann equations. We show that the standard formulation of superpotential method can be generalized. |
Booktitle |
Particle Physics On The Eve Of LHC: Proceedings of the Thirteenth Lomonosov Conference on Elementary Particle Physics |
Doi |
10.1142/9789812837592_0037 |
Language |
english |
Pages |
245--248 |
Publisher |
Singapore |
Tag |
Content |
Author |
Vernov, Sergey Yu. |
Title |
Construction of exact solutions in two-field cosmological models |
Year |
2008 |
Address |
Russian Federation |
Annote |
We construct a dark energy model with a phantom scalar field, a standard scalar field, and a polynomial potential inspired by string field theory. We find a two-parameter set of exact solutions of the Friedmann equations. We find a potential satisfying the conditions obtained from the string theory and such that at large times, some of the exact solutions correspond to the state parameter w(DE) > -1 while the others correspond to w(DE) < -1. We demonstrate that the superpotential method is very effective for seeking new exact solutions. |
Doi |
10.1007/s11232-008-0045-4 |
Issn |
1573-9333; 0040-5779 |
Journal |
Theoretical and Mathematical Physics |
Language |
english |
Number |
1 |
Pages |
544 --556 |
Publisher |
Russian Federation |
Volume |
155 |
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