Initial Value Problems for Integrable Systems on a Semi-Strip

Symmetry Integrability and Geometry-Methods and Applications

article

Alexander L. Sakhnovich¹ 

[1] Vienna University of Technology, Institute of Analysis and Scientific Computing

关键词: Weyl–Titchmarsh function;    initial condition;    quasi-analytic functions;    system on a semi-strip;    nonlinear Schr¨odinger equation;    nonlinear optics equation;   

DOI  :  10.3842/SIGMA.2016.001

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown