Abstract:
This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable deformations of meromorphic systems.
Bibliography: 40 titles.
Citation:
R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Russian Math. Surveys, 66:1 (2011), 63–105
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\by R.~R.~Gontsov, V.~A.~Poberezhnyi, G.~F.~Helminck
\paper On deformations of linear differential systems
\jour Russian Math. Surveys
\yr 2011
\vol 66
\issue 1
\pages 63--105
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Linking options:
https://www.mathnet.ru/eng/rm9404
https://doi.org/10.1070/RM2011v066n01ABEH004728
https://www.mathnet.ru/eng/rm/v66/i1/p65
This publication is cited in the following 6 articles:
Helminck G.F., Weenink J.A., “Integrable Hierarchies in the N X N-Matrices Related to Powers of the Shift Operator”, J. Geom. Phys., 148 (2020), 103560
G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “Strict versions of integrable hierarchies in pseudodifference operators and the related Cauchy problems”, Theoret. and Math. Phys., 198:2 (2019), 197–214
A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118
G. F. Helminck, A. G. Helminck, E. A. Panasenko, “Cauchy problems related to integrable deformations of pseudo differential operators”, J. Geom. Phys., 85 (2014), 196–205
Poberezhny V.A., “On deformations of linear systems of differential equations and the Painlevé property”, J. Math. Sci., 195:4 (2013), 533–540
Novikov D.P., Romanovskii R.K., Sadovnichuk S.G., Nekotorye novye metody konechnozonnogo integrirovaniya solitonnykh uravnenii, Nauka, Novosibirsk, 2013, 252 pp.
Citation in format AMSBIB
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