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Regular and Chaotic Dynamics, 2015, Volume 20, Issue 4, Pages 486–496
DOI: https://doi.org/10.1134/S1560354715040073 (Mi rcd28) 		 
This article is cited in 24 scientific papers (total in 24 papers)

On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions

Nikolay A. Kudryashov, Dmitry I. Sinelshchikov

National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409, Russia
Citations (24)
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DOI: https://doi.org/10.1134/S1560354715040073
Abstract: The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.
Keywords: quadratic lienard equation, elliptic functions, nonlocal transformations, general solution.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2296.2014.1
3694.2014.1
Russian Foundation for Basic Research 14-01-00498
14-01-31078
This research was partially supported by the grant for Scientific Schools 2296.2014.1, by the grant for the state support of young Russian scientists 3694.2014.1 and by RFBR grants 14–01–00498 and 14–01–31078.
Received: 29.05.2015
Bibliographic databases:
Document Type: Article
MSC: 34A34, 34A05, 33E05
Language: English
Citation: Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496
Citation in format AMSBIB
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\by Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
\paper On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 4
\pages 486--496
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    • This publication is cited in the following 24 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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