Peakons, kinks, compactons and solitary patterns solutions for a family of Camassa-Holm equations by using new hyperbolic schemes. (English) Zbl 1106.65109

Summary: A family of Camassa-Holm equations with distinct parameters is investigated. New solitary wave solutions that include peakons, kinks, compactons, solitary patterns solutions, and plane periodic solutions are formally derived. New schemes that rest mainly on hyperbolic functions are employed to achieve our goal. The work highlights the qualitative change in the physical structures of the obtained solutions.


65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
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