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Title: Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions

The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260 (United States)
  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
Publication Date:
OSTI Identifier:
22251032
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; EIGENFUNCTIONS; EQUATIONS; INVERSE SCATTERING PROBLEM; NONLINEAR PROBLEMS; RIEMANN SHEET; SCATTERING; SOLITONS; SPECTRA; SYMMETRY