2013/04/26 by Jiangbo Zhou, Zhou, Jiangbo, Lu Yao +5
Mathematics · Physics and Astronomy · #35B35 #35Q35 #35Q51 #37K45 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS) #math.AP #msc:35B35 #msc:35Q35 #msc:35Q51 #msc:37K45 #nlin.PS
paper · pdf · doi:10.48550/arxiv.1304.7084
Since the same result is already contained in the paper written by Changzheng Qu et al, this paper has been withdrawn by the authors. Many thanks for Prof. Qu's email
openalex publication_date 2013/04/26 · arxiv created 2013/05/01 · arxiv updated 2013/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we investigate the orbital stability problem of peakons for a modified Camassa-Holm equation with both quadratic and cubic nonlinearity. This equation was derived from integrable theory and admits peaked soliton (peakon) and multipeakon solutions. By constructing two suitable piecewise functions, we establish the polynomial inequality relating to two conserved quantities and the maximum of the solution to this equation. The error estimate between the maximum of the solution and the peakon then follows from the structure of the polynomial inequality. Finally, we prove that a wave starting close to the peakon remains close to some translate of it at all later times, that is, the shapes of these peakons are stable under small perturbations.