SIGMA, 2016, Volume 12, 001, 17 pages
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
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.
Weyl–Titchmarsh function; initial condition; quasi-analytic functions; system on a semi-strip; nonlinear Schrödinger equation; nonlinear optics equation.
|Austrian Science Fund
|This research was supported by the Austrian Science Fund (FWF) under Grant No. P24301.
PDF file (428 kB)
MSC: 35Q55; 35Q60; 34B20; 35A02
Received: September 1, 2015; in final form December 28, 2015; Published online January 3, 2016
Alexander L. Sakhnovich, “Initial Value Problems for Integrable Systems on a Semi-Strip”, SIGMA, 12 (2016), 001, 17 pp.
Citation in format AMSBIB
\paper Initial Value Problems for Integrable Systems on a Semi-Strip
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Sakhnovich A.L., “Evolution of Weyl Functions and Initial-Boundary Value Problems”, Math. Model. Nat. Phenom., 11:2 (2016), 111–132
|Number of views:|