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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 001, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.001 (Mi sigma1083) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Initial Value Problems for Integrable Systems on a Semi-Strip

Alexander L. Sakhnovich

Vienna University of Technology, Institute of Analysis and Scientific Computing, Wiedner Hauptstr. 8, A-1040 Vienna, Austria
Full-text PDF (428 kB) Citations (2)
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DOI: https://doi.org/10.3842/SIGMA.2016.001
Abstract: Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix solutions of the defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schrödinger equation.) Next, a special case of the nonlinear optics ($N$-wave) equation is considered.
Keywords: Weyl–Titchmarsh function; initial condition; quasi-analytic functions; system on a semi-strip; nonlinear Schrödinger equation; nonlinear optics equation.
Funding agency Grant number
Austrian Science Fund P24301
This research was supported by the Austrian Science Fund (FWF) under Grant No. P24301.
Received: September 1, 2015; in final form December 28, 2015; Published online January 3, 2016
Bibliographic databases:
Document Type: Article
MSC: 35Q55; 35Q60; 34B20; 35A02
Language: English
Citation: Alexander L. Sakhnovich, “Initial Value Problems for Integrable Systems on a Semi-Strip”, SIGMA, 12 (2016), 001, 17 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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