Bounded wave solutions of a generalized BBM equation with positive exponents

The traveling waves of a generalized BBM equation with positive exponents have been investigated in this Letter. The influence of the parameters on the number as well as the characteristics of the equilibrium points have been discussed in detail. Qualitatively different kinds of phase portraits have been explored with the variations of the parameters. All the possible bounded waves have been obtained, including periodic waves, kink-waves and solitons. For the special parameter conditions, the exact explicit expressions of waves have been presented in the end.