Orbital stability of periodic peakons for a quintic \mu ~modified-Camassa-Holm equation

We study the orbital stability of periodic peakons for a generalized \mu -modified-Camassa-Holm equation with quintic nonlinearities, which is a \mu -version for a generalized Camassa–Holm equation with quintic nonlinearities. First, we derive such equation via variational principle throw a modified Lagrangian, then we show the quintic \mu mCH equation admits periodic peakons, and finally we prove that the periodic peakons of quintic \mu mCH equation are orbitally stable under small perturbations in the H^1 space.