Deriving the New Traveling Wave Solutions for the Nonlinear Dispersive Equation, KdV-ZK Equation and Complex Coupled KdV System Using Extended Simplest Equation Method

Abstract

In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov–Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.

Exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov equation

“…This equation is also one of the basic models of ion‐acoustic solitons in which the hot isothermal electrons are defined by a Boltzmann distribution 1,2 . The solutions of the KdV–ZK equation have been investigated by the several different methods such as basic Lie symmetry 3 and extended simplest equation 4 methods.…”