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 speeds ci − ci−1 is large enough, to cancel all interactions.

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. 2014. ⟨hal-01111847v1⟩