On the criteria for integrability of the Liénard equation

Abstract

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

References in corpus (3)

• Analytical solutions for problems of bubble dynamics
• Analytical solutions of the Rayleigh equation for empty and gas--filled bubble
• Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations

Cited by in corpus (5)

• On the integrability conditions for a family of the Liénard-type equations
• New non-standard Lagrangians for the Liénard-type equations
• On connections of the Liénard equation with some equations of Painlevé--Gambier type
• Sundman transformation and alternative tangent structuresSundman transformation and alternative tangent structures
• Isochronous waveforms of Liénard equations via commutative factorization