Initial Value Problems for Integrable Systems on a Semi-Strip

2014/05/31 by Alexander L. Sakhnovich · 1 citation
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.CA #math.MP #math.SP #nlin.SI #msc:35Q55 #msc:35Q60 #msc:34B20 #msc:35A02

paper · pdf · doi:10.3842/sigma.2016.001

published as SIGMA 12 (2016), 001, 17 pages · Boundary conditions are recovered from the initial ones. The paper supplements in this respect our previous article arXiv:1403.8111, where initial conditions are recovered from the boundary conditions

arxiv created 2016/01/03 · arxiv updated 2016/01/05

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.

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