Stability of the $\mu$-Camassa-Holm Peakons
Robin Ming Chen, Jonatan Lenells, Yue Liu
TL;DR
This paper proves that the peakon solutions of the $$-Camassa-Holm equation are orbitally stable, contributing to the understanding of the stability properties of these nonlinear wave solutions.
Contribution
It establishes the orbital stability of periodic peaked traveling wave solutions (peakons) for the $$-Camassa-Holm equation, a significant result in the analysis of this integrable PDE.
Findings
Peakons are orbitally stable under the $$-Camassa-Holm dynamics.
The stability proof leverages the integrable structure of the equation.
Results extend the understanding of wave stability in nonlinear PDEs.
Abstract
The -Camassa-Holm (CH) equation is a nonlinear integrable partial differential equation closely related to the Camassa-Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the CH equation are orbitally stable.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Sphingolipid Metabolism and Signaling