dc.contributor.author Correia S. en_US dc.contributor.author Côte R. en_US dc.contributor.author Vega L. en_US dc.date.accessioned 2018-07-28T10:25:22Z dc.date.available 2018-07-28T10:25:22Z dc.date.issued 2018-07-06 dc.identifier.uri http://hdl.handle.net/20.500.11824/831 dc.description.abstract We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. Such knowledge is crucial in the study of stability properties of the self-similar solutions for the modified Korteweg-de Vries flow. In the defocusing case, the self-similar profiles are solutions to the PainlevéII equation. Although they were extensively studied in physical space, no result to our knowledge describe their behavior in Fourier space. We are able to relate the constants involved in the description in Fourier space with those involved in the description in physical space. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.relation info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.relation ES/1PE/SEV-2013-0323 en_US dc.relation ES/1PE/MTM2014-53850-P en_US dc.relation EUS/BERC/BERC.2014-2017 en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.title Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation en_US dc.type info:eu-repo/semantics/article en_US dc.type info:eu-repo/semantics/submittedVersion en_US dc.identifier.arxiv arXiv:1807.02302 dc.relation.publisherversion https://arxiv.org/abs/1807.02302 en_US
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