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Long, Yao; Li, Zhenyang; Rui, Weiguo

New travelling wave solutions for a nonlinearly dispersive wave equation of Camassa-Holm equation type. (English) Zbl 1203.35235

Appl. Math. Comput. 217, No. 4, 1315-1320 (2010).
Summary: The integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa-Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.

Cited in 5 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems
35C08 Soliton solutions
35B10 Periodic solutions to PDEs

Keywords:

nonlinearly dispersive wave equation of Camassa-Holm equation type; integral bifurcation method; loop soliton solution; periodic loop soliton solution; solitary wave solution; solitary cusp wave solution
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\textit{Y. Long} et al., Appl. Math. Comput. 217, No. 4, 1315--1320 (2010; Zbl 1203.35235)
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References:

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