𝑮′/𝑮, 𝟏/𝑮)-expansion method for analytical solutions of Jimbo-Miwa equation

Abstract

The main goal of this study is obtaining analytical solutions for (3+1)-dimensional Jimbo- Miwa Equation which the second equation in the well-known KP hierarchy of integrable systems. For the (3+1DJM) equation, hyperbolic, trigonometric, complex trigonometric and rational traveling wave solutions have been constructed by applying the (𝐺′/𝐺, 1/𝐺)- expansion method. Then, real and imaginary graphics are presented by giving special values to the constants in the solutions obtained. These graphics are a special solution of the (3+1DJM) equation and represent a stationary wave of the equation. The (𝐺′/𝐺, 1/𝐺)- expansion method is an effective and powerful method for solving nonlinear evolution equations (NLEEs). Ready computer package program is used to obtain the solutions and graphics presented in this study.