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The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebrogeometric 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. 157178.  Subject:  Exactly Solvable and Integrable Systems; Mathematical Physics; Algebraic Geometry; Analysis of PDEs  nlin.SI hepth mathph 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 initialboundary 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 pointlike sources, we show that the above boundary value problems can be rewritten as nonlinear dynamical systems for suitable sets of algebrogeometric 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 zeroboundary 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 righthand side.  Source:  arXiv, nlin.SI/0307026  Services:  Forum  Review  PDF  Favorites 


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