Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces

The long-time behaviour of solutions to the defocussing modified Korteweg-de Vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin thr...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 10
Main Authors Chen, Gong, Liu, Jiaqi
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2022
Subjects
Approximation
Asymptotic properties
Differential Equations
Initial conditions
Korteweg-Devries equation
Sobolev space
Steepest descent method
35C20
35Q53
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Summary:The long-time behaviour of solutions to the defocussing modified Korteweg-de Vries (MKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method of Deift and Zhou and its reformulation by Dieng and McLaughlin through $\overline {\partial }$ -derivatives. To extend the asymptotics to solutions with initial data in lower-regularity spaces, we apply a global approximation via PDE techniques.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2022.63