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On holomorphic solutions of equations of Korteweg-de Vries type


Author: A. V. Domrin
Translated by: V. E. Nazaikinskii
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva.
Journal: Trans. Moscow Math. Soc. 2012, 193-206
MSC (2010): Primary 35Q53; Secondary 30B40
DOI: https://doi.org/10.1090/S0077-1554-2013-00206-X
Published electronically: March 21, 2013
MathSciNet review: 3184975
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that, for any of the equations indicated in the title, every solution locally holomorphic in $ x$ and $ t$ admits global meromorphic continuation in $ x$ for each $ t$ with trivial monodromy at each pole. By way of application, we describe all possible envelops of meromorphy of local holomorphic solutions of the Boussinesq equation.


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Additional Information

A. V. Domrin
Affiliation: Faculty of Mechanics and Mathematics, Moscow State University, 1 Leninskie Gory, 119991 Moscow, Russian Federation
Email: domrin@mi.ras.ru

DOI: https://doi.org/10.1090/S0077-1554-2013-00206-X
Keywords: Soliton equation, holomorphic solution, analytic continuation
Received by editor(s): July 28, 2012
Published electronically: March 21, 2013
Additional Notes: Supported by RFBR grants nos. 11-01-12033-ofi-m, 11-01-00495-a-2011, and 10-01-00178-a
Article copyright: © Copyright 2013 American Mathematical Society

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