Exact Solutions To The Generalized Lienard Equations

TL;DR

This paper derives exact solitary wave solutions for the generalized Lienard equations by mapping them to $$-field theory and demonstrates their applicability to perturbed soliton equations and other nonlinear equations.

Contribution

It introduces a method to find exact solutions of generalized Lienard equations and shows these solutions also solve various perturbed and generalized nonlinear equations.

Findings

Exact solitary wave solutions for generalized Lienard equations

Solutions also solve perturbed soliton equations

Solutions applicable to other nonlinear equations

Abstract

Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the $\phi^6-$field theory. Further, it is shown that the exact solutions of the Lienard equation are also the exact solutions of the various perturbed soliton equations. Besides, we also consider a one parameter family of generalised Lienard equations and obtain exact solitary wave solutions of these equations and show that these are also the exact solutions of the various other generalised nonlinear equations.