dc.contributor.author | Eychenne, Arnaud | |
dc.date.accessioned | 2024-08-07T09:08:28Z | |
dc.date.available | 2024-08-07T09:08:28Z | |
dc.date.created | 2023-11-09T12:06:11Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0213-2230 | |
dc.identifier.uri | https://hdl.handle.net/11250/3145026 | |
dc.description.abstract | We construct N-soliton solutions for the fractional Korteweg–de Vries (fKdV) equation
∂tu−∂x(∣D∣αu−u2)=0,
in the whole sub-critical range α∈(1/2,2). More precisely, if Qc denotes the ground state solution associated to (fKdV) evolving with velocity c, then, given 0<c1<⋯<cN, we prove the existence of a solution U of (fKdV) satisfying
t→∞lim
U(t,⋅)−j=1∑NQcj(x−ρj(t))
Hα/2=0,
where ρj′(t)∼cj as t→+∞. The proof adapts the construction of Martel in the generalized KdV setting [Amer. J. Math. 127 (2005), pp. 1103–1140] to the fractional case. The main new difficulties are the polynomial decay of the ground state Qc and the use of local techniques (monotonicity properties for a portion of the mass and the energy) for a non-local equation. To bypass these difficulties, we use symmetric and non-symmetric weighted commutator estimates. The symmetric ones were proved by Kenig, Martel and Robbiano [Annales de l’IHP Analyse Non Linéaire 28 (2011), pp. 853–887], while the non-symmetric ones seem to be new. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | EMS Press | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Asymptotic N -soliton-like solutions of the fractional Korteweg–de Vries equation | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2022 Real Sociedad Matemática Española | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.doi | 10.4171/RMI/1396 | |
dc.identifier.cristin | 2194499 | |
dc.source.journal | Revista matemática iberoamericana | en_US |
dc.source.pagenumber | 1813-1862 | en_US |
dc.identifier.citation | Revista matemática iberoamericana. 2023, 39 (5), 1813-1862. | en_US |
dc.source.volume | 39 | en_US |
dc.source.issue | 5 | en_US |