The KdV equation on the half-line: The Dirichlet to Neumann map
In: Journal of Physics A, Jg. 46 (2013), Heft 34
Online
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Zugriff:
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.
Titel: |
The KdV equation on the half-line: The Dirichlet to Neumann map
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Autor/in / Beteiligte Person: | Lenells, Jonatan |
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Zeitschrift: | Journal of Physics A, Jg. 46 (2013), Heft 34 |
Veröffentlichung: | 2013 |
Medientyp: | unknown |
ISSN: | 1751-8113 (print) ; 1751-8121 (print) |
DOI: | 10.1088/1751-8113/46/34/345203 |
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