Approximate homotopy series solutions of perturbed PDEs via approximate symmetry method

TL;DR

This paper establishes a connection between approximate symmetry and homotopy methods for perturbed PDEs, enabling the derivation of series solutions through a transformation, demonstrated on the Cahn-Hilliard equation.

Contribution

It reveals a transformation linking approximate symmetry and homotopy methods, facilitating solution generation for perturbed PDEs.

Findings

Transformation connects approximate symmetry and homotopy equations.

Series solutions can be obtained by applying the transformation.

Application to Cahn-Hilliard equation confirms effectiveness.

Abstract

We show that the two couple equations derived by approximate symmetry method and approximate homotopy symmetry method are connected by a transformation for the perturbed PDEs. Consequently, approximate homotopy series solutions can be obtained by acting the transformation on the known solutions by approximate symmetry method. Applications to the Cahn-Hilliard equation illustrate the effectiveness of the transformation.