Initial Value Problems for Integrable Systems on a Semi-Strip
Analysis of PDEs
2016-01-05 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Spectral Theory
Exactly Solvable and Integrable Systems
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 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.
Cite
@article{arxiv.1405.3500,
title = {Initial Value Problems for Integrable Systems on a Semi-Strip},
author = {Alexander L. Sakhnovich},
journal= {arXiv preprint arXiv:1405.3500},
year = {2016}
}
Comments
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