Stability of peakons for the Degasperis-Procesi equation
Abstract
Description
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.
21 pages, to appear in Comm. Pure Appl. Math
21 pages, to appear in Comm. Pure Appl. Math