Initial Value Problems for Integrable Systems on a Semi-Strip

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.

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

References in corpus (1)

• Weyl functions and the boundary value problem for a matrix nonlinear Schrödinger equation on a semi-strip

Cited by in corpus (1)

• Evolution of Weyl functions and initial-boundary value problems