A SIMPLE JUSTIFICATION OF TANH METHOD FOR DISCRETE SOLITARY WAVE SOLUTIONS

The tanh method is known as an effective method for solving partial differential equations and obtaining traveling wave solutions. While well-used in continuous systems, its application to discrete systems (nonlinear difference-differential equations, DDEs) is still less explored. This paper revisits the tanh method for discrete systems, providing a simple justification for the method to produce discrete solitary wave solutions, including pulse-type and (anti)kink-type. By transforming DDEs into nonlinear ordinary differential equations (ODEs) and using polynomial forms in terms of the tanh function, we outline steps for deriving and verifying exact solutions