Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations | Zendy

Shaoyong Li | Zendy; Zhengrong Liu | Zendy

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Some Further Results on Traveling Wave Solutions for the ZK-BBM() Equations

Author(s) -

Shaoyong Li,

Zhengrong Liu

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/156139

Subject(s) - peakon , periodic wave , trigonometric functions , mathematical analysis , elliptic function , mathematics , limit (mathematics) , hyperbolic function , traveling wave , function (biology) , geometry , integrable system , evolutionary biology , biology

We investigate the traveling wave solutions for the ZK-BBM() equations 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

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