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Grébert, B; Kappeler, T (2002). Symmetries of the nonlinear Schrödinger equation. Societe Mathematique de France. Bulletin, 130(4):603-618.

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Abstract

Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum ⋯<λ k - ≤λ k + <λ k+1 - ≤⋯ of a Zakharov-Shabat operator is symmetric, i.e. λ k ± =-λ -k ∓ for all k, if and only if the sequence (γ k ) k∈ℤ of gap lengths, γ k :=λ k + -λ k - , is symmetric with respect to k=0.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Uncontrolled Keywords:NLS equation, Zakharov-Shabat operators, action-angle variables, symmetries
Language:English
Date:2002
Deposited On:18 Feb 2010 13:13
Last Modified:28 Nov 2013 00:35
Publisher:Societe Mathematique de France
ISSN:0037-9484
Additional Information:© 2002 SMF
Official URL:http://smf4.emath.fr/Publications/Bulletin/130/html/smf_bull_130_603-618
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1947455
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1044.35088

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