BIBLIOS

Tipo
Artigos em Revista

Tipo de Documento
Artigo Completo

Título
Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

Participantes na publicação
Simão Correia (Author)
Dep. Matemática
CMAFcIO
Raphaël Côte (Author)
Luis Vega (Author)

Resumo
We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although they were extensively studied in physical space, no result to our knowledge describe their behavior in Fourier space. These Fourier asymptotics are crucial in the study of stability properties of the self-similar solutions for the modified Korteweg-de Vries flow.\\\\\\\\\\\\\\\\n\\\\\\\\\\\\\\\\nOur result is obtained through a fixed point argument in a weighted space around a carefully chosen, two term ansatz, and we are able to relate the constants involved in the description in Fourier space with those of the description in physical space.


Instituição
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Suporte
Journal de Mathématiques Pures et Appliquées

Identificadores da Publicação
ISSN - 0021-7824

Editora
Elsevier BV



Identificadores do Documento
DOI - https://doi.org/10.1016/j.matpur.2020.03.013
URL - http://dx.doi.org/10.1016/j.matpur.2020.03.013

Identificadores de Qualidade
Web Of Science Q1 (2020) - 2.464 - MATHEMATICS - SCIE
SCIMAGO Q1 (2020) - 2.526 - Applied Mathematics