Symbolic methods to construct a cusp, breathers, kink, rogue waves and some soliton waves solutions of nonlinear partial differential equations

Abstract

A cusp, bright breathers, dark breathers, kink, bright rogue waves and some soliton waves solutions are obtained by using the $exp(-phi(xi))$-expansion method for the fourth order Benjamin-Ono equation and BBM equations. The obtained solutions might be indicated and meaningful for narrating the physical phenomena in the real-world. For compatible values of the arbitrary parameter included in the solution, We plot the 3D surface of the all obtained solutions in this paper which are shown in Figures 1 to 10.