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Regular version of the site

Article

New non-standard Lagrangians for the Lienard-type equations

Applied Mathematics Letters. 2017. Vol. 63. P. 124-129.
Кудряшов Н. А., Sinelshchikov D.

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.