BIBLIOS

Document type
Journal articles

Document subtype
Full paper

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

Participants in the publication
Simão Correia (Author)
Dep. Matemática
CMAFcIO
Raphaël Côte (Author)
Luis Vega (Author)

Summary
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.


Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Where published
Journal de Mathématiques Pures et Appliquées

Publication Identifiers
ISSN - 0021-7824

Publisher
Elsevier BV



Document Identifiers
DOI - https://doi.org/10.1016/j.matpur.2020.03.013
URL - http://dx.doi.org/10.1016/j.matpur.2020.03.013

Rankings
Web Of Science Q1 (2020) - 2.464 - MATHEMATICS - SCIE
SCIMAGO Q1 (2020) - 2.526 - Applied Mathematics