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

Journal Article · Mon Jun 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4922362· OSTI ID:22479686

Bertola, Marco ^[1]; Giavedoni, Pietro ^[2]

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1. Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve W., Montréal, Québec H3G1M8 (Canada)
2. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien (Austria)

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.

• OSTI ID: 22479686
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
RIEMANN SHEET
SCHROEDINGER EQUATION
SOLITONS