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

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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.

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Authors and Affiliations

  1. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe sh. 31, Moscow, 115409, Russia

    Nikolay A. Kudryashov & Dmitry I. Sinelshchikov

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  1. Nikolay A. Kudryashov
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  2. Dmitry I. Sinelshchikov
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Correspondence to Nikolay A. Kudryashov.

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Kudryashov, N.A., Sinelshchikov, D.I. On the connection of the quadratic Lienard equation with an equation for the elliptic functions. Regul. Chaot. Dyn. 20, 486–496 (2015). https://doi.org/10.1134/S1560354715040073

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  • DOI: https://doi.org/10.1134/S1560354715040073

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