On the new hyperbolic and trigonometric structures to the simplified MCH and SRLW equations

Abstract

With the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is used in constructing some new solutions to the two well-known nonlinear models, namely, the simplified modified Camassa-Holm and symmetric regularized long-wave equations. We obtain some novel complex, trigonometric and hyperbolic function solutions to these two equations. We also plot the three-dimensional and two-dimensional graphics for each solutions obtained using the same programming code in Wolfram Mathematica software. Finally, we submit a comprehensive conclusions.