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

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4868483· OSTI ID:22251032

Biondini, Gino ^[1]; Kovačič, Gregor ^[2]

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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)

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.

• OSTI ID: 22251032
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
EIGENFUNCTIONS
EQUATIONS
INVERSE SCATTERING PROBLEM
NONLINEAR PROBLEMS
RIEMANN SHEET
SCATTERING
SOLITONS
SPECTRA
SYMMETRY