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Initial Value Problems for Integrable Systems on a Semi-Strip
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 Schr\"odinger equation
with quasi-analytic boundary conditions is dealt with. (The result is new even
for a scalar nonlinear Schr\"odinger equation.) Next, a special case of the
nonlinear optics (-wave) equation is considered.Comment: 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 condition
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