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dc.contributor.authorCorreia S.en_US
dc.contributor.authorCôte R.en_US
dc.contributor.authorVega L.en_US
dc.date.accessioned2018-07-28T10:25:22Z
dc.date.available2018-07-28T10:25:22Z
dc.date.issued2018-07-06
dc.identifier.urihttp://hdl.handle.net/20.500.11824/831
dc.description.abstractWe 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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.relationinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.relationES/1PE/SEV-2013-0323en_US
dc.relationES/1PE/MTM2014-53850-Pen_US
dc.relationEUS/BERC/BERC.2014-2017en_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.titleAsymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equationen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/submittedVersionen_US
dc.identifier.arxivarXiv:1807.02302
dc.relation.publisherversionhttps://arxiv.org/abs/1807.02302en_US


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