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The KdV equation on the half-line: The Dirichlet to Neumann map
Baylor University, United States; University of Cambridge, United Kingdom .ORCID iD: 0000-0001-6191-7769
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 46, no 34, 345203Article in journal (Refereed) Published
Abstract [en]

We consider initial-boundary value problems for the KdV equation u t + ux + 6uux + uxxx = 0 on the half-line x 0. For a well-posed problem, the initial data u(x, 0) as well as one of the three boundary values {u(0, t), ux (0, t), uxx (0, t)} can be prescribed; the other two boundary values remain unknown. We provide a characterization of the unknown boundary values for the Dirichlet as well as the two Neumann problems in terms of a system of nonlinear integral equations. The characterizations are effective in the sense that the integral equations can be solved perturbatively to all orders in a well-defined recursive scheme.

Place, publisher, year, edition, pages
2013. Vol. 46, no 34, 345203
National Category
Physical Sciences Mathematics
URN: urn:nbn:se:kth:diva-163795DOI: 10.1088/1751-8113/46/34/345203ISI: 000322910800007ScopusID: 2-s2.0-84882411157OAI: diva2:802397

QC 20150417

Available from: 2015-04-13 Created: 2015-04-12 Last updated: 2015-04-17Bibliographically approved

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Lenells, Jonatan
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