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

A cusp, bright breathers, dark breathers, kink, bright rogue waves and some soliton waves solutions are obtained by using the exp(−ϕ(ξ))-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 realworld. For compatible values of the arbitrary parameter included in the solution, we plot the 3D surface of the all obtained solutions which are shown in Figure 1 to Figure 10.