We investigate the traveling wave solutions and their bifurcations for the BBM-like equations by using bifurcation method and numerical simulation approach of dynamical systems. Firstly, for BBM-like 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 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.
"The Traveling Wave Solutions and Their Bifurcations for the BBM-Like Equations." J. Appl. Math. 2013 1 - 17, 2013. https://doi.org/10.1155/2013/490341