A SIMPLE JUSTIFICATION OF TANH METHOD FOR DISCRETE SOLITARY WAVE SOLUTIONS - Syarif, Ahmad; Syafwan, Mahdhivan; Nazra, Admi (Jurnal Lebesgue : Jurnal Ilmiah Pendidikan Matematika, Matematika dan Statistika, 2024)
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