Exact solutions for fifth-order KdV-type equations with time-dependent coefficients using the Kudryashov method

Abstract

The KdV equation plays an important role in describing motions of long waves in shallow water under gravity, one-dimensional nonlinear lattice, fluid mechanics, quantum mechanics, plasma physics, nonlinear optics and other areas. The KdV equation is a well-known model for the description of nonlinear long internal waves in a fluid stratified by both density and current. The aim of this paper is to present solitary wave solutions of the fifth-order KdV equations with time-dependent coefficients. The Kudryashov method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving high-order nonlinear partial differential equations with time-dependent coefficients in mathematical physics.