Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa-Holm equations

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4835395· OSTI ID:22251787

Li, Jibin ^[1]; Qiao, Zhijun ^[2]

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1. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004 (China)
2. Department of Mathematics, The University of Texas Pan-American, 1201 West University Drive, Edinburg, Texas 78541 (United States)

In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing.

• OSTI ID: 22251787
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CUSPED GEOMETRIES
EQUATIONS
MATHEMATICAL SOLUTIONS
PEAKS
PERIODICITY