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

Abstract

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.

Keywords:

• μ-Camassa–Holm equation
• periodic peakon
• orbital stability

AMS Mathematics Subject Classifications:

• 35G25
• 35B30

Disclosure statement

The author declares no conflicts of interest.

Additional information

Funding

This work was supported by the Scientific Research Start-Up Project of Shanxi Institute of Technology [grant number 2021QD-20]; the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [grant number 2021L593].