Initial Value Problems for Integrable Systems on a Semi-Strip

[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.

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