Homotopy Analysis of Korteweg-de Vries Equation with Time Delay

Abstract

The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces and it possesses both the periodic solutions (travelling wave solutions) and the solitary wave solutions. It is one of the most frequently encountered equations in the field of fluid mechanics due to its significant nature in physical context, stratified internal waves, ion-acoustic wave and plasma physics. The delay system has potential applications in waves as well and several works have been done for particular cases [1]. While the analytically periodic solutions with high precision can hardly obtained and such work has not been reported before. In this paper, we shall develop a newly analytical approach based on the homotopy analysis method (HAM) to such wave problems with delay system. With this method, it is expected to capture the analytical approximations with high accuracy and a general approach for such problems can be established systematically