Dispersive soliton solutions for shallow water wave system and modified Benjamin-Bona-Mahony equations via applications of mathematical methods

Abstract

We have utilized three novel methods, called generalized direct algebraic, modified F-expansion and improved simple equation methods to construct traveling wave solutions of the system of shallow water wave equations and modified Benjamin-Bona-Mahony equation. After substituting particular values of the parameters, different solitary wave solutions are derived from the exact traveling wave solutions. It is shown that these employed methods are more powerful tools for nonlinear wave equations.

Keywords

• System of shallow water wave equations
• Modified Benjamin-Bona-Mahony equation
• Generalized direct algebraic method
• Improved simple equation method
• Modified F-expansion method
• Traveling wave solutions