The Traveling Wave Solutions and Their Bifurcations for the BBM-Like B(m,n)‎ Equations

Abstract EN

We investigate the traveling wave solutions and their bifurcations for the BBM-like B(m,n) equations ut+αux+β(um)x−γ(un)xxt=0 by using bifurcation method and numerical simulation approach of dynamical systems.

Firstly, for BBM-like B(3,2) equation, we obtain some precise expressions of traveling wave solutions, which include periodic blow-up and periodic wave solution, peakon and periodic peakon wave solution, and solitary wave and blow-up solution.

Furthermore, we reveal the relationships among these solutions theoretically.

Secondly, for BBM-like B(4,2) equation, we construct two periodic wave solutions and two blow-up solutions.

In order to confirm the correctness of these solutions, we also check them by software Mathematica.