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Orbital stability of periodic peakons for the generalized modified Camassa-Holm equation. (English) Zbl 1480.35092

Summary: This paper is devoted to studying the dynamical stability of periodic peaked solitary waves for the generalized modified Camassa-Holm equation. The equation is a generalization of the modified Camassa-Holm equation and it possesses the Hamiltonian structure shared by the modified Camassa-Holm equation. The equation admits the periodic peakons. It is shown that the periodic peakons are dynamically stable under small perturbations in the energy space.

MSC:

35C08 Soliton solutions
35B10 Periodic solutions to PDEs
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
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