A Note on "M - component nonlinear evolution equations: multiple soliton solutions"

TL;DR

This paper critiques a previous study by showing it reduced complex M-component nonlinear evolution equations to well-known equations and used established methods, questioning the originality of the solutions presented.

Contribution

The paper clarifies that the previous work did not genuinely analyze M-component equations but instead focused on known equations with standard solution methods.

Findings

The original paper reduced M-component equations to known equations.

Hirota method was used for solutions of the reduced equations.

The study questions the novelty of the multiple soliton solutions presented.

Abstract

We analyze the recent paper by Wazwaz [Wazwaz A.M., M - component nonlinear evolution equations: multiple soliton solutions, Phys. Scr. 81 (2010) 055004]. We demonstrate that author did not consider in essence the M - component nonlinear evolution equations but he reduced the M - component equations to the well - known Korteweg - de Vries equation, to modified Korteweg - de Vries equation and to the Kadomtsev - Petviashvili equation. To find multiple soliton solutions for these well - known equations author has used the Hirota method.