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dc.creatorMuñoz, Claudio
dc.date2017-12-01
dc.date.accessioned2019-11-14T12:00:33Z
dc.date.available2019-11-14T12:00:33Z
dc.identifierhttps://www.revistaproyecciones.cl/article/view/2541
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/113429
dc.descriptionWe consider the focusing Nonlinear Schrödinger equation posed on the one dimensional line, with nonzero background condition at spatial infinity, given by a homogeneous plane wave. For this problem of physical interest, we study the initial value problem for perturbations of the background wave in Sobolev spaces. It is well-known that the associated linear dynamics for this problem describes a phenomenon known in the literature as modulational instability, also recently related to the emergence of rogue waves in ocean dynamics. In qualitative terms, small perturbations of the background state increase its size exponentially in time. In this paper we show that, even if there is no time decay for the linear dynamics due to the modulationally unstable regime, the equation is still locally well-posed in Hs, s > 1/2. We apply this result to give a rigorous proof of the unstable character of two well-known NLS solutions: the Peregrine and Kuznetsov-Mabreathers.  en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.es-ES
dc.relationhttps://www.revistaproyecciones.cl/article/view/2541/2143
dc.rightsDerechos de autor 2017 Proyecciones. Journal of Mathematicses-ES
dc.rightshttps://creativecommons.org/licenses/by-nc/4.0/es-ES
dc.sourceProyecciones. Journal of Mathematics; Vol 36 No 4 (2017); 653-683en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 36 Núm. 4 (2017); 653-683es-ES
dc.source0717-6279
dc.source0716-0917
dc.subjectModulationen-US
dc.subjectInstabilityen-US
dc.subjectWell-posednessen-US
dc.subjectSchrödingeren-US
dc.subjectPeregrineen-US
dc.subjectBreatheren-US
dc.titleInstability in nonlinear Schrödinger breathers.en-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArtículo revisado por pareses-ES


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