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, . . . , cN , such that the difference between consecutive locations of peakons is large enough.Comment: arXiv admin note: text overlap with arXiv:0803.0261 by other author

A Nonlinear Liouville Property for the Generalized Kawahara Equation

In this paper, by applying the method of Martel and Merle [9], we prove that the solution of the generalized Kawahara equation (gKW) which is close in the energy space H 2 (R) to the soliton (constructed by Kabakouala and Molinet [4]), and which is uniformely localized becomes identically equal to these soliton

A Remark on the Stability of Peakons for the Degasperis-Procesi Equation

International audienceIn this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1)

Asymptotic stability of the solitary waves for the generalized Kawahara equation

In Kabakouala and Molinet [7] we construct two families if solitary waves of the gKW equation and we prove that they are obitally stable. In this paper by applying the method of Martel and Merle [12] we prove that this families of solitary waves are asymptotically stable in the energy space

On the stability of the solitary waves to the (generalized) kawahara equation

In this paper we investigate the orbital stability of solitary waves to the (generalized) Kawahara equation (gKW) which is a fifth order dispersive equation. For some values of the power of the nonlinearity, we prove the orbital stability in the energy space H 2 (R) of two branches of even solitary waves of gKW by combining the well-known spectral method introduced by Benjamin [3] with continuity arguments. We construct the first family of even solitons by applying the implicit function theorem in the neighborhood of the explicit solitons of gKW found by Dey et al. [8]. The second family consists of even travelling waves with low speeds. They are solutions of a constraint minimization problem on the line and rescaling of perturbations of the soliton of gKdV with speed 1