Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method

Abstract

Mathematical modeling of many autonomous physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear evolution equations plays a significant role in the study of nonlinear physical phenomena. In this article, the enhanced (G′/G)-expansion method has been applied for finding the exact traveling wave solutions of longitudinal wave motion equation in a nonlinear magneto-electro-elastic circular rod. Each of the obtained solutions contains an explicit function of the variables in the considered equations. It has been shown that the applied method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering fields.

Construction of traveling wave solutions of the (2 + 1)‐dimensional modified KdV‐KP equation

“…The method is promising since it can provide a large range of innovative traveling wave solutions for a variety of physical nonlinear models. 31,33,34 We have derived the exact expression for the solitary waves that arise in the continuum modified KdV-KP model. The speed, as well as the profile of these solitary waves, is highly sensitive to the free parameters.…”

“…We use enhanced ‐expansion approach (studied in Khan et al 31,32 ) to solve the model (). The method is promising since it can provide a large range of innovative traveling wave solutions for a variety of physical nonlinear models 33,34 . We have derived the exact expressions for the solitary waves that arise in the continuum‐modified KdV‐KP model.…”