On the criteria for integrability of the Lienard equation

摘要

The Lienard 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 Lienard equation using an approach based on nonlocal transformations. We also obtain some of the previously known criteria for integrability of the Lienard equation as a straightforward consequence of our approach's application. We illustrate our results by several new examples of integrable Lienard equations. (C) 2016 Elsevier Ltd. All rights reserved.