On complete integrability for systems of differential equations

In this note we discuss the approach which was given by Wazwaz for proving the complete integrability to the system of nonlinear differential equations. We show that his method presented in [Wazwaz AM. Completely integrable coupled KdV and coupled KP systems. Commun Nonlinear Sci Simulat 2010;15:2828–35] is incorrect.