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 Tr. Mosk. Mat. Obs., 2014, Volume 75, Issue 2, Pages 205–218 (Mi mmo564)

Real-analytic solutions of the nonlinear Schrödinger equation

A. V. Domrin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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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English version:
Transactions of the Moscow Mathematical Society, 2014, 75, 173–183

Document Type: Article
UDC: 517.547.24+517.956.4
MSC: 35Q55, 37K15

Citation: A. V. Domrin, “Real-analytic solutions of the nonlinear Schrödinger equation”, Tr. Mosk. Mat. Obs., 75, no. 2, MCCME, M., 2014, 205–218; Trans. Moscow Math. Soc., 75 (2014), 173–183

Citation in format AMSBIB
\Bibitem{Dom14} \by A.~V.~Domrin \paper Real-analytic solutions of the nonlinear Schr\"odinger equation \serial Tr. Mosk. Mat. Obs. \yr 2014 \vol 75 \issue 2 \pages 205--218 \publ MCCME \publaddr M. \mathnet{http://mi.mathnet.ru/mmo564} \elib{http://elibrary.ru/item.asp?id=23780163} \transl \jour Trans. Moscow Math. Soc. \yr 2014 \vol 75 \pages 173--183 \crossref{https://doi.org/10.1090/S0077-1554-2014-00236-3} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84960117409}