| Stability of peakons for the Degasperis-Procesi equation (2007) | |||||||||
Abstract | |||||||||
| 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.. Comment: 21 pages, to appear in Comm. Pure Appl. Math | |||||||||
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