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Transactions of the Moscow Mathematical Society

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Real-analytic solutions of the nonlinear Schrödinger equation


Author: A. V. Domrin
Translated by: Christopher Hollings
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 75 (2014), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2014, 173-183
MSC (2010): Primary 35Q55, 37K15
Published electronically: November 5, 2014
MathSciNet review: 3308608
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Abstract | References | Similar Articles | Additional Information

Abstract: 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 Schrödinger 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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Additional Information

A. V. Domrin
Affiliation: Mechanics and Mathematics Faculty, Moscow State University
Email: domrin@mi.ras.ru

DOI: https://doi.org/10.1090/S0077-1554-2014-00236-3
Keywords: Nonlinear Schr\"odinger equation, local inverse scattering problem method, analytic extension
Published electronically: November 5, 2014
Additional Notes: This work was supported by the Russian Foundation for Basic Research (grants 14-01-00709-a, 13-01-00622-a, 13-01-12417-ofi-m) and by a grant from the Simons Foundation.
Article copyright: © Copyright 2014 A V. Domrin