English

On the criteria for integrability of the Li\'{e}nard equation

Exactly Solvable and Integrable Systems 2016-08-05 v1 Classical Analysis and ODEs

Abstract

The Li\'{e}nard equation is of a high importance from both mathematical and physical points of view. However a question about integrability of this equation has not been completely answered yet. Here we provide a new criterion for integrability of the Li\'{e}nard equation using an approach based on nonlocal transformations. We also obtain some of previously known criteria for integrability of the Li\'{e}nard equation as a straightforward consequences of our approach's application. We illustrate our results by several new examples of integrable Li\'{e}nard equations.

Keywords

Cite

@article{arxiv.1608.01636,
  title  = {On the criteria for integrability of the Li\'{e}nard equation},
  author = {Nikolai A. Kudryashov and Dmitry I. Sinelshchikov},
  journal= {arXiv preprint arXiv:1608.01636},
  year   = {2016}
}