On the criteria for integrability of the Li\'enard equation
Abstract
The Li\'enard 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\'enard equation using an approach based on nonlocal transformations. We also obtain some of previously known criteria for integrability of the Li\'enard equation as a straightforward consequences of our approach's application. We illustrate our results by several new examples of integrable Li\'enard equations.
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