On Completely Integrability Systems of Differential Equations

TL;DR

This paper critically examines Wazwaz's method for proving the complete integrability of certain nonlinear differential systems, demonstrating that his approach is flawed.

Contribution

It provides a critical analysis showing the incorrectness of Wazwaz's previously proposed method for establishing integrability.

Findings

Wazwaz's method is invalid for proving complete integrability.

The paper clarifies the limitations of the previous approach.

It emphasizes the need for correct proof techniques in integrability studies.

Abstract

In this note we discuss the approach which was given by Wazwaz for the proof of the complete integrability to the system of nonlinear differential equations. We show that his method presented in [Wazwaz A.M. Completely integrable coupled KdV and coupled KP systems, Commun Nonlinear Sci Simulat 15 (2010) 2828-2835] is incorrect.