Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane
2015 (English)In: Studies in applied mathematics (Cambridge), ISSN 0022-2526, E-ISSN 1467-9590Article in journal (Refereed) Published
The unified transform method introduced by Fokas can be used to analyze initial-boundary value problems for integrable evolution equations. The method involves several steps, including the definition of spectral functions via nonlinear Fourier transforms and the formulation of a Riemann-Hilbert problem. We provide a rigorous implementation of these steps in the case of the mKdV equation in the quarter plane under limited regularity and decay assumptions. We give detailed estimates for the relevant nonlinear Fourier transforms. Using the theory of L2-RH problems, we consider the construction of quarter plane solutions which are C1 in time and C3 in space.
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IdentifiersURN: urn:nbn:se:kth:diva-176204DOI: 10.1111/sapm.12089ISI: 000368781700002ScopusID: 2-s2.0-84956832222OAI: oai:DiVA.org:kth-176204DiVA: diva2:873118
QC 201511232015-11-232015-11-022016-02-23Bibliographically approved