Approximate homotopy symmetry method and homotopy series solutions to the six-order boussinesq equation

TL;DR

This paper introduces an approximate homotopy symmetry method for nonlinear equations, specifically applied to the six-order Boussinesq equation, providing a systematic way to derive series solutions and similarity reductions.

Contribution

The paper develops a novel approximate homotopy symmetry approach that generalizes existing methods and allows adjustable convergence regions for solutions of complex nonlinear equations.

Findings

Derived general formulas for similarity reduction solutions

Obtained homotopy series solutions with adjustable convergence

Showed that series solutions can be retrieved from approximate symmetry methods

Abstract

An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the six-order boussinesq equation. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. The convergence region of homotopy series solutions can be adjusted by the auxiliary parameter. Series solutions and similarity reduction equations from approximate symmetry method can be retrieved from approximate homotopy symmetry method.