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The Nonlinear Steepest Descent Method for Riemann-Hilbert Problems of Low Regularity
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2017 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 66, no 4, p. 1287-1332Article in journal (Refereed) Published
Abstract [en]

We prove a nonlinear steepest descent theorem for Riemann-Hilbert problems with Carleson jump contours and jump matrices of low regularity and slow decay. We illustrate the theorem by deriving the long-time asymptotics for the mKdV equation in the similarity sector for initial data with limited decay and regularity.

Place, publisher, year, edition, pages
Department of Mathematics, Indiana University , 2017. Vol. 66, no 4, p. 1287-1332
Keywords [en]
Nonlinear steepest descent, Riemann-Hilbert problem, asymptotic analysis, long time asymptotics
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-221050DOI: 10.1512/iumj.2017.66.6078ISI: 000418808700008Scopus ID: 2-s2.0-85032286612OAI: oai:DiVA.org:kth-221050DiVA, id: diva2:1172937
Funder
Swedish Research Council, 2015-05430EU, European Research Council, 682537
Note

QC 20180111

Available from: 2018-01-11 Created: 2018-01-11 Last updated: 2018-01-11Bibliographically approved

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Lenells, Jonatan

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