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

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,…,cNc1,…,cN, such that the difference between consecutive locations of peakons is large enough.