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

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.


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
Full Text: DOI


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