On the homotopy perturbation method for Boussinesq-like equations

TL;DR

This paper critically examines the homotopy perturbation method for Boussinesq-like equations, demonstrating that similar solutions can be obtained via Taylor series and questioning the significance of a superposition principle.

Contribution

It shows that solutions obtained by the homotopy perturbation method can be replicated with Taylor series, and discusses the limitations of the superposition principle in this context.

Findings

Homotopy perturbation method solutions match Taylor series results.

Superposition principle may lack mathematical and physical significance.

General solutions derived using travelling waves.

Abstract

We comment on some analytical solutions to a class of Boussinesq-like equations derived recently by means of the homotopy perturbation method (HPM). We show that one may obtain exactly the same result by means of the Taylor series in the time variable. We derive more general results by means of travelling waves and argue that a curious superposition principle may not be of any mathematical or physical significance.