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Initial value problems for integrable systems on a semi-strip. (English) Zbl 1345.35107

The author studies two integrable equations on a semi-strip \(\mathcal{D}=\{(x,t):0\leq x<\infty, 0\leq t<a\}\) where boundary conditions and solutions are uniquely determined by initial conditions: the matrix-valued defocusing nonlinear Schrödinger equation with quasi-analytic boundary conditions and a special case of the nonlinear optics equation (\(N\)-wave equation). The paper is a continuation of the paper [J. Math. Anal. Appl. 423, No. 1, 746–757 (2015; Zbl 1308.35280)] by the same author.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
34B20 Weyl theory and its generalizations for ordinary differential equations
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Citations:

Zbl 1308.35280
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References:

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