Some Further Results on Traveling Wave Solutions for the ZK-BBM(m, n) Equations. (2nd November 2013) - Li, Shaoyong
Abstract : We investigate the traveling wave solutions for the ZK-BBM(m, n ) equations u t + u x - a u m x + b u n x t + k u n y t x = 0 by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2) equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2) equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.