Stability of periodic peakons for a generalized-μ Camassa–Holm equation with quartic nonlinearities.

In this paper, we study the stability of periodic peakons for a generalized-μ-Camassa–Holm (μQCH) equation with quartic nonlinearity. The equation is a μ-version of a generalized Camassa–Holm equation with quartic nonlinearities. First, we derive such equation via variational principle throw a modified Lagrangian, then we show the μQCH equation admits periodic peakons, and finally we prove that the periodic peakons of μQCH equation are orbitally stable under small perturbations in the energy space. [ABSTRACT FROM AUTHOR]