非线性Schrödinger方程的实解析解

Q2 Mathematics

Transactions of the Moscow Mathematical Society Pub Date : 2014-11-05 DOI:10.1090/S0077-1554-2014-00236-3

A. Domrin

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引用次数: 4

摘要

．建立了酉对称形式矩阵值洛朗级数分解的黎曼问题有解。作为一个应用，我们证明了聚焦非线性Schr¨odinger方程的任何局部实解析解(在x和t上)都有一个实解析扩展到平行于x轴的条上，并且在每个这样的条上都存在一个不能进一步扩展的解。

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Real-analytic solutions of the nonlinear Schrödinger equation

. We establish that the Riemann problem on the factorization of formal matrix-valued Laurent series subject to unitary symmetry has a solution. As an application, we show that any local real-analytic solution (in x and t ) of the focusing nonlinear Schr¨odinger equation has a real-analytic extension to some strip parallel to the x -axis and that in each such strip there exists a solution that cannot be extended further.

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来源期刊

Transactions of the Moscow Mathematical Society Mathematics-Mathematics (miscellaneous)

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期刊介绍： This journal, a translation of Trudy Moskovskogo Matematicheskogo Obshchestva, contains the results of original research in pure mathematics.