Stability of peakons for a modified Camassa-Holm equation
Xingxing Liu, Zhaoyang Yin
TL;DR
This paper proves the orbital stability of peakons in a modified Camassa-Holm equation with cubic nonlinearity, derived from the 2D Euler equation, by overcoming conservation law difficulties with a new auxiliary function.
Contribution
It introduces a novel approach using an auxiliary function to establish stability, addressing challenges posed by complex conservation laws.
Findings
Peakons are orbitally stable under the modified equation.
The new method overcomes difficulties from conservation laws.
The stability proof applies to a cubic nonlinearity context.
Abstract
In this paper, we investigate the orbital stability of peakons for a modified Camassa-Holm equation with cubic nonlinearity derived from the two-dimensional Euler equation. By overcoming the difficulties caused by one of the complicated conservation laws and introducing a new auxiliary function, we prove the orbital stability of peakons for the equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Algebraic structures and combinatorial models