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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 2, Pages 328–340
DOI: https://doi.org/10.4213/tmf9472 (Mi tmf9472) 		 
This article is cited in 11 scientific papers (total in 11 papers)

On integrable non–autonomous Liénard–type equations

D. I. Sinelshchikov, N. A. Kudryashov

National Research Nuclear University "MEPhI", Moscow, Russia
Full-text PDF (507 kB) Citations (11)
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DOI: https://doi.org/10.4213/tmf9472
Abstract: We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct general traveling-wave and stationary solutions of certain classes of diffusion–convection equations. We also illustrate our results with several other examples of integrable nonautonomous Liénard-type equations.
Keywords: Liénard-type equation, nonlocal transformation, general solution, Painlevé–Gambier equation.
Funding agency Grant number
Russian Science Foundation 17-71-10241
This research is supported by a grant from the Russian Science Foundation (Project No. 17-71-10241).
Received: 29.09.2017
Revised: 11.11.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 2, Pages 1230–1240
DOI: https://doi.org/10.1134/S0040577918080093
Bibliographic databases:
PACS: 02.30.Hq; 02.30.Ik
MSC: 34A05; 34A34; 34M55
Language: Russian
Citation: D. I. Sinelshchikov, N. A. Kudryashov, “On integrable non–autonomous Liénard–type equations”, TMF, 196:2 (2018), 328–340; Theoret. and Math. Phys., 196:2 (2018), 1230–1240
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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