Orbital Stability of Periodic Peakons to a Generalized μ-Camassa-Holm Equation

摘要

In this paper, we study the orbital stability of the periodic peaked solitons of the generalized μ-Camassa-Holm equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Camassa-Holm equation and themodified Camassa-Holm equation. It is also integrable with the Lax-pair and bi-Hamiltonian structure and admits the single peakons and multipeakons. By constructing an inequality related to the maximum and minimum of solutions with the conservation laws, we prove that, even in the case that the Camassa-Holm energy counteracts in part the modified Camassa-Holm energy, the shapes of periodic peakons are still orbitally stable under small perturbations in the energy space.