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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

 

On the poles of Picard potentials


Author: A. V. Komlov
Translated by: Alex Martsinkovsky
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 71 (2010).
Journal: Trans. Moscow Math. Soc. 2010, 241-250
MSC (2010): Primary 34M45; Secondary 35Q51, 35Q53
Published electronically: December 21, 2010
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Abstract: We study the existence of a global meromorphic fundamental system of solutions for a system of two differential equations $ E_{x} = (az +q(x))E$, where $ a$ is a constant diagonal matrix, and $ q(x)$ is an off-diagonal meromorphic function, for each $ z \in \mathbb{C}$. Following Gesztesy and Weikard (1998), who investigated this property of functions $ q(x)$ and its connection to finite-gap solutions of soliton equations, we call such $ q(x)$ Picard potentials. We obtain conditions for the Picard property of various potentials $ q(x)$.


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Additional Information

A. V. Komlov
Affiliation: M. V. Lomonosov Moscow State University
Email: komlov@hotbox.ru

DOI: http://dx.doi.org/10.1090/S0077-1554-2010-00182-3
PII: S 0077-1554(2010)00182-3
Published electronically: December 21, 2010
Additional Notes: Supported by the RFFI Grant 08–01–00014 and by the Support Program for Leading Scientific Schools Grant NSh-3877.2008.1
Article copyright: © Copyright 2010 American Mathematical Society