Analytical and numerical solutions to the (3

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. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

Automated summary

In this paper, analytical solutions for a significant nonlinear partial differential equation with variable coefficients were found using the Exp-function method and extended tanh method, while numerical solutions were also obtained through the finite difference method. The results highlighted the effectiveness of the methods used, and various types of solutions were obtained by adjusting constant parameters. Through comparison tables and graphs, the accuracy of the methods applied was demonstrated.