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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| Published in | Forum of mathematics. Sigma Vol. 10 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Cambridge, UK
Cambridge University Press
01.01.2022
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| ISSN | 2050-5094 2050-5094 |
| DOI | 10.1017/fms.2022.63 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| ArticleNumber | e66 |
| Author | Chen, Gong Liu, Jiaqi |
| Author_xml | – sequence: 1 givenname: Gong surname: Chen fullname: Chen, Gong email: gc@math.gatech.edu organization: School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Skiles Building, Atlanta, GA; E-mail: gc@math.gatech.edu – sequence: 2 givenname: Jiaqi surname: Liu fullname: Liu, Jiaqi email: jqliu@ucas.ac.cn organization: School of Mathematics, University of the Chinese Academy of Sciences, No. 19 Yuquan Road, Beijing, China; E-mail: jqliu@ucas.ac.cn |
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| Cites_doi | 10.1098/rsta.1975.0035 10.1007/978-3-642-58045-1_10 10.1016/j.aim.2016.04.023 10.2307/2946540 10.1007/BF02570720 10.1016/j.matpur.2009.01.012 10.1215/S0012-7094-01-10638-8 10.1002/cpa.3160460405 10.1137/0520065 10.1090/S0894-0347-03-00421-1 10.1016/j.anihpc.2017.08.006 10.57262/die/1356019601 10.1155/S1073792899000203 10.1002/cpa.3160480304 10.1016/j.anihpc.2021.02.008 10.1215/S0012-7094-06-13524-X 10.1016/j.anihpc.2017.04.002 10.1007/s00220-018-3138-4 10.1023/A:1012953917956 10.1080/00036811.2013.866227 10.1215/00127094-2018-0033 10.1002/cpa.3034 10.1007/s00039-018-0444-0 10.1002/(SICI)1097-0312(199807)51:7<697::AID-CPA1>3.0.CO;2-1 10.1353/ajm.2003.0040 10.1137/0520091 10.1063/1.531706 10.1007/BF02761431 10.1080/03605302.2015.1114495 |
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| SubjectTerms | Approximation Asymptotic properties Differential Equations Initial conditions Korteweg-Devries equation Sobolev space Steepest descent method |
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| Title | Long-time asymptotics of the modified KdV equation in weighted Sobolev spaces |
| URI | https://www.cambridge.org/core/product/identifier/S2050509422000639/type/journal_article https://www.proquest.com/docview/2705207267 |
| Volume | 10 |
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