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Airy and Painleve asymptotics for the mKdV equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6191-7769
2019 (English)In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750Article in journal (Refereed) Published
Abstract [en]

We consider the higher order asymptotics for the modified Korteweg-de Vries equation in the Painleve sector. We first show that the solution admits a uniform expansion to all orders in powers of t-1/3 with coefficients that are smooth functions of x(3t)-1/3. We then consider the special case when the reflection coefficient vanishes at the origin. In this case, the leading coefficient which satisfies the Painleve II equation vanishes. We show that the leading asymptotics are instead described by the derivative of the Airy function. We are also able to express the subleading term explicitly in terms of the Airy function.

Place, publisher, year, edition, pages
Wiley , 2019.
Keywords [en]
37K15, 41A60, 35Q15, 35Q53 (primary)
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-257450DOI: 10.1112/jlms.12265ISI: 000480198900001OAI: oai:DiVA.org:kth-257450DiVA, id: diva2:1348416
Note

QC 20190904

Available from: 2019-09-04 Created: 2019-09-04 Last updated: 2019-09-04Bibliographically approved

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Charlier, ChristopheLenells, Jonatan

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