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25 February 2020
 
  » arxiv » nlin.SI/0307026

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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’’
AbstractThis 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
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