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Asymptotic stability of solitons for mKdV

Author(s): Germain, Pierre; Pusateri, Fabio Giuseppe; Rousset, Frederic

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Abstract: We prove a full asymptotic stability result for solitary wave solutions of the mKdV equation. We consider small perturbations of solitary waves with polynomial decay at infinity and prove that solutions of the Cauchy problem evolving from such data tend uniformly, on the real line, to another solitary wave as time goes to infinity. We describe precisely the asymptotes of the perturbation behind the solitary wave showing that it satisfies a nonlinearly modified scattering behavior. This latter part of our result relies on a precise study of the asymptotic behavior of small solutions of the mKdV equation. (C) 2016 Elsevier Inc. All rights reserved.
Publication Date: 20-Aug-2016
Electronic Publication Date: 26-May-2016
Citation: Germain, Pierre, Pusateri, Fabio, Rousset, Frederic. (2016). Asymptotic stability of solitons for mKdV. ADVANCES IN MATHEMATICS, 299 (272 - 330. doi:10.1016/j.aim.2016.04.023
DOI: doi:10.1016/j.aim.2016.04.023
ISSN: 0001-8708
EISSN: 1090-2082
Pages: 272 - 330
Type of Material: Journal Article
Journal/Proceeding Title: ADVANCES IN MATHEMATICS
Version: Author's manuscript

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