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New non-standard Lagrangians for the Liénard-type equations

Liénard-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 Liénard-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 Liénard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.

preprint2016arXivOpen access
Nikolai A. KudryashovDmitry I. Sinelshchikov
nlin.SI
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Nikolai A. KudryashovDmitry I. Sinelshchikov

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