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Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs
Baylor University, United States.ORCID iD: 0000-0001-6191-7769
2012 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 241, no 8, 857-875 p.Article in journal (Refereed) Published
Abstract [en]

We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve 3×3 matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse Scattering Transform (IST), the presence of a boundary presents new challenges. Over the last fifteen years, an extension of the IST formalism developed by Fokas and his collaborators has been successful in analyzing boundary value problems for several of the most important integrable equations with 2×2 Lax pairs, such as the Kortewegde Vries, the nonlinear Schrdinger, and the sine-Gordon equations. In this paper, we extend these ideas to the case of equations with Lax pairs involving 3×3 matrices.

Place, publisher, year, edition, pages
2012. Vol. 241, no 8, 857-875 p.
Keyword [en]
Initial-boundary value problem, Integrable system, Inverse scattering, Riemann-Hilbert problem, Evolution equations, Initial-boundary value problems, Integrable equations, Inverse scattering transform, Korteweg-de Vries, Lax pairs, Riemann Hilbert problems, Initial value problems, Nonlinear equations, Differential equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-163808DOI: 10.1016/j.physd.2012.01.010ISI: 000302759400005Scopus ID: 2-s2.0-84858282504OAI: oai:DiVA.org:kth-163808DiVA: diva2:802385
Note

QC 20150427

Available from: 2015-04-13 Created: 2015-04-12 Last updated: 2017-12-04Bibliographically approved

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Lenells, Jonatan

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