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arXiv · 1608.04926

New non-standard Lagrangians for the Li\'enard-type equations

Nikolai A. Kudryashov·Dmitry I. Sinelshchikov
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Abstract

Li\'enard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Li\'enard-type equations which admits a non-standard autonomous Lagrangian. As a by-product we obtain autonomous first integrals for each member of this family of equations. We also show that some of the previously known conditions for the existence of a non-standard Lagrangian for the Li\'enard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.

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Nikolai A. Kudryashov, Dmitry I. Sinelshchikov. 2016-08-17. New non-standard Lagrangians for the Li\'enard-type equations. https://doi.org/10.1016/j.aml.2016.07.028

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