Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2003-07-16
American Mathematical Society Translations - Series 2, Advances in the Mathematical Sciences, 2004, v. 212., pp. 157-178.
Nonlinear Sciences
Exactly Solvable and Integrable Systems
29 pages, LaTeX, 2 Encapsulated Postscript figures
Scientific paper
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 Schr\"odinger 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.
Grinevich Petr G.
Santini Paolo Maria
No associations
LandOfFree
The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The initial boundary value problem on the segment for the Nonlinear Schrödinger equation; the algebro-geometric approach. I will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-207476