|
Эта публикация цитируется в 19 научных статьях (всего в 19 статьях)
Exact Solutions and Integrability of the Duffing–Van der Pol Equation
Nikolay A. Kudryashov
Department of Applied Mathematics, National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia
Аннотация:
The force-free Duffing–Van der Pol oscillator is considered. The truncated expansions for finding the solutions are used to look for exact solutions of this nonlinear ordinary differential equation. Conditions on parameter values of the equation are found to have the linearization of the Duffing–Van der Pol equation. The Painlevé test for this equation is used to study the integrability of the model. Exact solutions of this differential equation are found. In the special case the approach is simplified to demonstrate that some well-known methods can be used for finding exact solutions of nonlinear differential equations. The first integral of the Duffing–Van der Pol equation is found and the general solution of the equation is given in the special case for parameters of the equation. We also demonstrate the efficiency of the method for finding the first integral and the general solution for one of nonlinear second-order ordinary differential equations.
Ключевые слова:
Duffing–Van der Pol oscillator, Painlevé test, exact solution, truncated expansion, singular manifold, general solution
| Финансовая поддержка |
Номер гранта |
Российский научный фонд  |
18-11-00209 |
| This research was supported by Russian Science Foundation Grant No. 18-11-00209 "Development of methods for investigation of nonlinear mathematical models". |
DOI:
https://doi.org/10.1134/S156035471804007X
 Список литературы:
PDF файл
HTML файл
Реферативные базы данных:
  
Тип публикации:
Статья
MSC: 34M25
Поступила в редакцию: 01.05.2018
Принята в печать:04.06.2018
Язык публикации: английский
Образец цитирования:
Nikolay A. Kudryashov, “Exact Solutions and Integrability of the Duffing–Van der Pol Equation”, Regul. Chaotic Dyn., 23:4 (2018), 471–479
Цитирование в формате AMSBIB
\RBibitem{Kud18}
\by Nikolay A. Kudryashov
\paper Exact Solutions and Integrability of the Duffing–Van der Pol Equation
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 4
\pages 471--479
\mathnet{http://mi.mathnet.ru/rcd334}
\crossref{https://doi.org/10.1134/S156035471804007X}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3836282}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000440806900007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85051065239}
Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd334 http://mi.mathnet.ru/rus/rcd/v23/i4/p471
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
-
N. A. Kudryashov, “On Integrability of the FitzHugh – Rinzel Model”, Нелинейная динам., 15:1 (2019), 13–19
  -
Nikolay A. Kudryashov, Dariya V. Safonova, Anjan Biswas, “Painlevé Analysis and a Solution to the Traveling Wave Reduction of the Radhakrishnan – Kundu – Lakshmanan Equation”, Regul. Chaotic Dyn., 24:6 (2019), 607–614
-
W. Liu, Yu. Zhang, A. M. Wazwaz, Q. Zhou, “Analytic study on triple-s, triple-triangle structure interactions for solitons in inhomogeneous multi-mode fiber”, Appl. Math. Comput., 361 (2019), 325–331
 -
N. A. Kudryashov, “First integrals and general solution of the fokas-lenells equation”, Optik, 195 (2019), 163135
-
N. A. Kudryashov, “Solitary and periodic waves of the hierarchy for propagation pulse in optical fiber”, Optik, 194 (2019), 163060
-
N. A. Kudryashov, “Construction of nonlinear differential equations for description of propagation pulses in optical fiber”, Optik, 192 (2019), 162964
-
N. A. Kudryashov, “Traveling wave reduction of the modified KdV hierarchy: the Lax pair and the first integrals”, Commun. Nonlinear Sci. Numer. Simul., 73 (2019), 472–480
-
N. A. Kudryashov, “Lax pair and first integrals of the traveling wave reduction for the KdV hierarchy”, Appl. Math. Comput., 350 (2019), 323–330
-
N. A. Kudryashov, “Traveling wave solutions of the generalized nonlinear Schrödinger equation with cubic-quintic nonlinearity”, Optik, 188 (2019), 27–35
-
N. A. Kudryashov, “General solution of traveling wave reduction for the Kundu–Mukherjee–Naskar model”, Optik, 186 (2019), 22–27
-
N. A. Kudryashov, “General solution of the traveling wave reduction for the perturbed Chen–Lee–Liu equation”, Optik, 186 (2019), 339–349
-
N. A. Kudryashov, “First integrals and general solution of the traveling wave reduction for Schrödinger equation with anti-cubic nonlinearity”, Optik, 185 (2019), 665–671
-
N. A. Kudryashov, “A generalized model for description of propagation pulses in optical fiber”, Optik, 189 (2019), 42–52
-
N. A. Kudryashov, “The first integrals and exact solutions of a two-component Belousov–Zhabotinskii reaction system”, VII International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012030
-
N. A. Kudryashov, “First integrals and solutions of the traveling wave reduction for the Triki–Biswas equation”, Optik, 185 (2019), 275–281
-
N. A. Kudryashov, “Exact solutions of the equation for surface waves in a convecting fluid”, Appl. Math. Comput., 344 (2019), 97–106
-
N. A. Kudryashov, “On general solutions of two nonlinear ordinary differential equations”, International Conference on Numerical Analysis and Applied Mathematics (ICNAAM-2018), AIP Conf. Proc., 2116, eds. T. Simos, C. Tsitouras, Amer. Inst. Phys., 2019, 270002
-
N. A. Kudryashov, “Remarks on the Fuchs indices and the first integrals for nonlinear ordinary differential equations”, VII International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012031
-
Oswaldo González-Gaxiola, Anjan Biswas, Mir Asma, Abdullah Kamis Alzahrani, “Optical Dromions and Domain Walls with the Kundu – Mukherjee – Naskar Equation by the Laplace – Adomian Decomposition Scheme”, Regul. Chaotic Dyn., 25:4 (2020), 338–348
|
| Просмотров: |
| Эта страница: | 128 | | Литература: | 20 |
|
Пользовательское соглашение