dc.contributor.author | Martel, Yvan | |
dc.contributor.author | Pilod, Didier Jacques Francois | |
dc.date.accessioned | 2021-08-06T11:33:53Z | |
dc.date.available | 2021-08-06T11:33:53Z | |
dc.date.created | 2020-09-16T11:54:58Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0010-3616 | |
dc.identifier.uri | https://hdl.handle.net/11250/2766804 | |
dc.description.abstract | For the critical generalized KdV equation ∂tu+∂x(∂2xu+u5)=0 on R, we construct a full family of flattening solitary wave solutions. Let Q be the unique even positive solution of Q′′+Q5=Q. For any ν∈(0,13), there exist global (for t≥0) solutions of the equation with the asymptotic behavior
u(t,x)=t−ν2Q(t−ν(x−x(t)))+w(t,x)
where, for some c>0,
x(t)∼ct1−2ν and ∥w(t)∥H1(x>12x(t))→0 as t→+∞.
Moreover, the initial data for such solutions can be taken arbitrarily close to a solitary wave in the energy space. The long-time flattening of the solitary wave is forced by a slowly decaying tail in the initial data. This result and its proof are inspired and complement recent blow-up results for the critical generalized KdV equation. This article is also motivated by previous constructions of exotic behaviors close to solitons for other nonlinear dispersive equations such as the energy-critical wave equation. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Full family of flattening solitary waves for the critical generalized KdV 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 2020 The Authors | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 2 | |
dc.identifier.doi | 10.1007/s00220-020-03815-z | |
dc.identifier.cristin | 1830389 | |
dc.source.journal | Communications in Mathematical Physics | en_US |
dc.source.pagenumber | 1011-1080 | en_US |
dc.identifier.citation | Communications in Mathematical Physics. 2020, 378, 1011-1080. | en_US |
dc.source.volume | 378 | en_US |