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This article is cited in 1 scientific paper (total in 1 paper)
The One-Dimensional Riemann Problem on an Elliptic Curve
A. A. Matveevaa, V. A. Poberezhnyiab a National Research University "Higher School of Economics" (HSE), Moscow
b State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow
Abstract:
A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.
Keywords:
Riemann problem, elliptic curve, logarithmic connection.
Author to whom correspondence should be addressed
DOI:
https://doi.org/10.4213/mzm11107
Full text:
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English version:
Mathematical Notes, 2017, 101:1, 115–122
Bibliographic databases:
UDC:
517.925.7
PACS:
02.30.Zz Received: 26.06.2016 Revised: 09.08.2016
Citation:
A. A. Matveeva, V. A. Poberezhnyi, “The One-Dimensional Riemann Problem on an Elliptic Curve”, Mat. Zametki, 101:1 (2017), 91–100; Math. Notes, 101:1 (2017), 115–122
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/mz11107https://doi.org/10.4213/mzm11107 http://mi.mathnet.ru/eng/mz/v101/i1/p91
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This publication is cited in the following articles:
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A. A. Matveeva, V. A. Poberezhny, “Two-dimensional Riemann problem for rigid representations on an elliptic curve”, J. Geom. Phys., 114 (2017), 384–393
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