English

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

Exactly Solvable and Integrable Systems 2016-08-18 v1

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.

Keywords

Cite

@article{arxiv.1608.04926,
  title  = {New non-standard Lagrangians for the Li\'enard-type equations},
  author = {Nikolai A. Kudryashov and Dmitry I. Sinelshchikov},
  journal= {arXiv preprint arXiv:1608.04926},
  year   = {2016}
}

Comments

To appear in Applied Mathematics Letters