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Stability of peakons for the Degasperis‐Procesi equation
Author(s) -
Lin Zhiwu,
Liu Yue
Publication year - 2009
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20239
Subject(s) - peakon , mathematics , camassa–holm equation , stability (learning theory) , lyapunov function , mathematical analysis , euler's formula , exponential stability , euler equations , function (biology) , integrable system , physics , nonlinear system , computer science , quantum mechanics , machine learning , evolutionary biology , biology
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 Lyapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations. © 2007 Wiley Periodicals, Inc.