Analytical and numerical solutions to the (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients

Abstract

In this paper, we implemented the Exp-function method and the extended tanh method to finds the analytical solutions of one of the important nonlinear partial differential equations with variable coefficients called the new (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients. Moreover, we find the numerical solutions to that equation using the finite difference method. The results demonstrate the effectiveness and convenience of the used methods. Comparison between our results through some tables and graphs to illustrate the accuracy of the applied methods. We obtained the different types of solutions-like bright, dark, periodic, rational and singular periodic soliton solutions using the different values of constant parameters. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in (3 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa with time-dependent coefficients model.