Study of the Supercritical Solution of the Stationary Negative Forced KdV Equation

Abstract

This paper we considers Forced KdV equation with negative forcing term. The supercritical solitary wave solutions of the stationary Forced KdV equations are obtained. In order to obtain the solutions the domain of the problem has been divided into three parts; the left, the middle and the right parts. The solution on the left and the right parts are obtained by an analytical method. The solution on the middle part is expressed in terms of Weierstarss elliptic function. A computer programs using Mathematica is designed to produce the solutions. The complete solution is found by matching the solutions of all the three parts. It is found that there are four different solutions according to the values of the phase shift. All solutions are positive. Keywords: Stationary Forced KdV Equation; Supercritical solution.