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Title: A degeneration of two-phase solutions of the focusing nonlinear Schrödinger equation via Riemann-Hilbert problems

Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime, such solutions reduce to some elementary ones called “Solitons on unstable condensate.” This degeneration turns out to be conveniently studied by means of basic tools from the theory of Riemann-Hilbert problems. In particular, no acquaintance with Riemann surfaces and theta-function is required for such analysis.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve W., Montréal, Québec H3G1M8 (Canada)
  2. (Canada)
  3. (Italy)
  4. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien (Austria)
Publication Date:
OSTI Identifier:
22479686
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; RIEMANN SHEET; SCHROEDINGER EQUATION; SOLITONS