Multi-soliton of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation and KdV equation

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the soliton solutions are also found. Furthermore, three-dimensional plots of the wave solutions and its potential functions are given to visualize the dynamics of the model and their energy. We also provided the corresponding density plot of the solutions to understand the real direction and particles density in the waves which help to realize the elastic situations of the achieved solutions.