On some invariant solutions of (2+1)-dimensional Korteweg–de Vries equations

Abstract

In the present research, similarity transformation method is proposed to obtain some more general invariant solutions of (2+1)-dimensional Korteweg–de Vries equations. This system of equations describes nonlinear waves propagation on the surface of shallow water. The method reduces the number of independent variables by one using invariance property of Lie group theory. Thus, Korteweg–de Vries equations are reduced into a system of ordinary differential equations employing twice of similarity transformation method. This system of ordinary differential equations is solved under some parametric restrictions and provides invariant solutions. The obtained results are supplemented by numerical simulation taking suitable choice of arbitrary constants and functions. Eventually, the elastic behavior of multisoliton, compacton, negaton, positon, kink wave solution and dromion annihilation profiles are shown to make this research more admirable.