Some Further Results on Traveling Wave Solutions for the ZK-BBM(m, n) Equations. (2nd November 2013)

• Record Type: Journal Article
• Authors: Li, Shaoyong; Liu, Zhengrong
• Other Names: Govinder K. S. Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-11-02
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/156139
• Languages: English
• ISSNs: 1110-757X

Abstract

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.