Conservation Laws and Travelling Wave Solutions for a Negative-Order KdV-CBS Equation in 3+1 Dimensions

Abstract

In this paper, we study a new negative-order KdV-CBS equation in (3 + 1) dimensions which is a combination of the Korteweg-de Vries (KdV) equation and Calogero-Bogoyavlenskii-Schiff (CBS) equation. Firstly, we determine the Lie point symmetries of the equation and conservation laws by using the multiplier method. The conservation laws will be used to obtain a triple reduction to a second order ordinary differential equation (ODE), which lead to line travelling waves and soliton solutions. Such solitons are obtained via the modified form of simple equation method and are displayed through three-dimensional plots at specific parameter values to lend physical meaning to nonlinear phenomena. It illustrates that these solutions might be extremely beneficial in understanding physical phenomena in a variety of applied mathematics areas.