UZH-Logo

Symmetries of the nonlinear Schrödinger equation


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

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.

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.

Citations

4 citations in Web of Science®
4 citations in Scopus®
Google Scholar™

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification: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:05 Apr 2016 13:25
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

Download

Full text not available from this repository.

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations