The Application of the exp⁡(-Φ(ξ))-Expansion Method for Finding the Exact Solutions of Two Integrable Equations

Abstract

In this article, the exp⁡-Φξ method is connected to search for new hyperbolic, periodic, and rational solutions of (1+1)-dimensional fifth-order nonlinear integrable equation and (2+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. The obtained solutions consist of trigonometric, hyperbolic, rational functions and W-shaped soliton. Furthermore, 3D and 2D graphs are plotted by choosing the suitable values of the parameters involved.