- - - School of Mathematical Sciences, University of Science and Technology of China, ۲۳۰۰۲۶, Hefei, China.
- - - School of Mathematical Sciences, University of Science and Technology of China, ۲۳۰۰۲۶, Hefei, China.

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 ۳D surface of the all obtained solutions in this paper which are shown in Figures ۱ to ۱۰.

The exp(-phi(xi))-expansion method, the fourth order Benjamin-Ono equation, BBM equation, traveling wave solutions, Nonlinear evolution equation