Abstract
Considered in this paper is a higher-order μ-Camassa-Holm equation. As a prototype, this higher-order μ-Camassa-Holm equation can be viewed as a generalization of the μ-Camassa-Holm equation. Periodic peaked waves of this higher-order μ-Camassa-Holm equation have been established to be H1-orbitally stable. By utilizing the method of characteristics, we prove the nonlinear instability of peaked perturbations to the H1-orbitally stable periodic peakons. Furthermore, a delicate analysis is employed to show that small initial W1,∞(S1) perturbations of the above periodic peakons lead to the blow-up phenomenon in finite time in the nonlinear evolution of the higher-order μ-Camassa-Holm equation.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
