Classifications of Soliton Solutions of the Generalized Benjamin-Bona-Mahony Equation with Power-Law Nonlinearity

Abstract

In this work, the order reduction technique and He's variational principle are used for exact solutions of the nonlinearly dispersive generalized Benjamin-Bona-Mahony (shortly BBM(m,n)) equation with power-law nonlinearity. Therefore, we acquire compactons, solitary patterns, solitary wave and periodic wave solutions for this equation. We illustrate that the analytical methods are very efficient to present the physical behaviors of the solutions of nonlinear evolution equations. Additionally, the constraint conditions for the existence of these solutions are presented.