New non-standard Lagrangians for the Liénard-type equations

Abstract

Liénard-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 Liénard-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 Liénard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.

To appear in Applied Mathematics Letters

References in corpus (4)

• Lagrangians Galore
• On the criteria for integrability of the Liénard equation
• Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations
• Using an old method of Jacobi to derive Lagrangians: a nonlinear dynamical system with variable coefficients

Cited by in corpus (1)

• Sundman transformation and alternative tangent structuresSundman transformation and alternative tangent structures