Stability in the energy space of the sum of N peakons for the Degasperis–Procesi equation

André Kabakouala (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

The Degasperis-Procesi equation possesses well-known peaked solitary waves that are called peakons. Their stability has been established by Lin and Liu in [5]. In this paper, we localize the proof (in some suitable sense detailed in Section 3) of the stability of a single peakon. Thanks to this, we extend the result of stability to the sum of N peakons traveling to the right with respective speeds c1, . . . , cN , such that the difference between consecutive locations of peakons is large enough.

Mots clés: Degasperis-Procesi Equation; Stability; Peakons

Domaines: Equations aux dérivées partielles [math.AP]

André Kabakouala. Stability in the energy space of the sum of N peakons for the Degasperis–Procesi equation. Electronic Journal of Differential Equations, 2015, 259 (5), pp.1841--1897. ⟨10.1016/j.jde.2015.03.014⟩. ⟨hal-01111847v3⟩