Some further results on traveling wave solutions for the ZK-BBM(m,n) equations

We investigate the traveling wave solutions for the zk-bbm(m,n) equations ut+ux-aumx+bunxt+kunytx=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. © 2013 shaoyong li and zhengrong liu.