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Initial boundary value problems for the nonlinear Schrödinger equation

Pelloni, B. (2000) Initial boundary value problems for the nonlinear Schrödinger equation. Theoretical and Mathematical Physics, 122 (1). pp. 107-120. ISSN 0040-5779

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To link to this article DOI: 10.1007/BF02551174

Abstract/Summary

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical and Physical Sciences > Department of Mathematics and Statistics
ID Code:7543
Publisher:Springer Verlag

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