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.
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.
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
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\paper On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions
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\yr 2015
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\issue 4
\pages 486--496
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Linking options:
https://www.mathnet.ru/eng/rcd28
https://www.mathnet.ru/eng/rcd/v20/i4/p486
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