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SIGMA, 2016, Volume 12, 001, 17 pages (Mi sigma1083)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.


DOI: https://doi.org/10.3842/SIGMA.2016.001

Full text: PDF file (428 kB)
Full text: http://www.emis.de/journals/SIGMA/2016/001/
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Bibliographic databases:

ArXiv: 1405.3500
Document Type: Article
MSC: 35Q55; 35Q60; 34B20; 35A02
Received: September 1, 2015; in final form December 28, 2015; Published online January 3, 2016
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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sakhnovich A.L., “Evolution of Weyl Functions and Initial-Boundary Value Problems”, Math. Model. Nat. Phenom., 11:2 (2016), 111–132  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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