The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I

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This is the first of a series of papers devoted to the study of classical initial-boundary value problems of Dirichlet, Neumann and mixed type for the Nonlinear Schrödinger equation on the segment. Considering proper periodic discontinuous extensions of the profile, generated by suitable point-like sources, we show that the above boundary value problems can be rewritten as nonlinear dynamical systems for suitable sets of algebro-geometric spectral data, generalizing the classical Dubrovin equations. In this paper we consider, as a first illustration of the above method, the case of the Dirichlet problem on the segment with zero-boundary value at one end, and we show that the corresponding dynamical system for the spectral data can be written as a system of ODEs with algebraic right-hand side.
29 pages, LaTeX, 2 Encapsulated Postscript figures

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Exactly Solvable and Integrable Systems, High Energy Physics - Theory, Mathematical Physics, Algebraic Geometry, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/80530

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0307026
 http://arxiv.org/abs/nlin/0307026
 American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, 2004, v. 212., pp. 157-178.

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arXiv