2007/12/12 by Zhiwu Lin, Yue Liu, Lin, Zhiwu +1 · 1 citation
Mathematics · Physics and Astronomy · #35G35 #35Q51 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #math-ph #math.AP #math.MP #msc:35G35 #msc:35Q51
paper · pdf · doi:10.48550/arxiv.0712.2007
21 pages, to appear in Comm. Pure Appl. Math
arxiv created 2007/12/12 · openalex publication_date 2007/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis-Procesi equation on the line. By constructing a Liapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations.