Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions

Abstract

The Jaulent–Miodek (JM) system is investigated analytically in this study. The JM equation comes with energy-dependent Schrödinger potential which is used in fluid dynamics, optics, condensed matter physics and engineering systems. As a result, it is critical to investigate this dynamical problem from a mathematical point of view. The generalized exponential rational function method is applied to extract the exact solutions of JM system. These exact traveling wave solutions are successfully extracted in the form of trigonometric, hyperbolic, rational, and exponential functions. The suitable choices of parameters are granted to draw the plots of some solutions. The physical behaviors of these solutions are shown physically, which are helpful to understand the physical phenomena of these dynamical model which are arisen in the mathematical physics.