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Regular and Chaotic Dynamics

, Volume 20, Issue 4, pp 486–496 | Cite as

On the connection of the quadratic Lienard equation with an equation for the elliptic functions

  • Nikolay A. Kudryashov
  • Dmitry I. Sinelshchikov
Article

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 

MSC2010 numbers

34A34 34A05 33E05 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • Nikolay A. Kudryashov
    • 1
  • Dmitry I. Sinelshchikov
    • 1
  1. 1.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

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