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The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I | | P.G.Grinevich
; P.M.Santini
; | | Date: |
16 Jul 2003 | | Journal: | American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, 2004, v. 212., pp. 157-178. | | Subject: | Exactly Solvable and Integrable Systems; Mathematical Physics; Algebraic Geometry; Analysis of PDEs | nlin.SI hep-th math-ph math.AG math.AP math.MP | | Affiliation: | L.D.Landau Institute for Theoretical Physics, Dipartimento di Fisica, Università di Roma ``La Sapienza’’ | | Abstract: | 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. | | Source: | arXiv, nlin.SI/0307026 | | Services: | Forum | Review | PDF | Favorites | |
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