Alexander Sakhnovich
Published 2014-05-14, updated 2015-08-31Version 2
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 Schroedinger equation with quasi-analytic boundary conditions is dealt with. (The result is new even for a scalar nonlinear Schroedinger equation.) Next, a special case of the nonlinear optics (N-wave) equation is considered.
Comments: In this paper, 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. Several explanations and references are added in the second version of the paper
Non-concentration of quasimodes for integrable systems
Initial value problems for wave equations on manifolds
Spectral theory for self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the defocusing nonlinear Schroedinger equation with periodic boundary conditions
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