Factorization and Lie point symmetries of general Lienard-type equation in the complex plane

TL;DR

This paper introduces a variational method to linearize and factorize a general Lienard-type equation in the complex plane, exemplified by the Van der Pol oscillator, and explores its Lie point symmetries.

Contribution

It presents a novel variational approach for linearizing and factorizing Lienard-type equations, along with analyzing their Lie point symmetries.

Findings

Successfully linearized the Lienard-type equation

Factorized the almost linear equation

Derived Lie algebraic generators for symmetries

Abstract

We present a variational approach to a general Lienard-type equation in order to linearize it and, as an example, the Van der Pol oscillator is discussed. The new equation which is almost linear is factorized. The point symmetries of the deformed equation are also discussed and the two-dimensional Lie algebraic generators are obtained.