The new complex travelling wave solutions of the simplified modified camassa holm equation

Abstract

The simplified modified Camassa Holm (SMCH) equation is an essential nonlinear model for classifying several wave phenomena in physical science. In this study, the new (M+1/G ')-expansion method has been applied to the SMCH equation. Based on the given method, we have obtained some typical analytical solutions, such as exponential and rational function and complex function solutions of the SMCH equation. The three-dimensional and contour graphs of the obtained results are drawn for appropriate values of parameters. Getting the results and graphic drawings have been made using the Wolfram Mathematica. All the obtained solutions are crucial for understanding the nonlinear phenomena of dispersive waves. The solutions have shown that the presented method is powerful, practical, and suitable for investigating nonlinear models.