Soliton-like solutions of general variable coefficient (2+1)-dimensional KdV equation with linear damping term

Abstract

A general variable coefficient (2+1)-dimensional KdV equation with linear damping term (VC(2+1)d damping KdV equation for short) has been investigated by using the simplified homogeneous balance method. It has been proven firstly that if the coefficients of the equation satisfy a certain constraint condition, then the VC(2+1)d damping KdV equation has a nonlinear transformation that converts the VC(2+1)d damping KdV equation itself into a homogeneous quadratic equation which admits a series of exponential function solutions. By means of the nonlinear transformation derived here, one and two soliton-like solutions of the VC(2+1)d damping KdV equation are obtained successfully. As an illustrative example, a concrete VC(2+1)d damping KdV equation is studied, the nonlinear transformation, and one and two soliton-like solutions of the equation are all given.