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This article is cited in 7 scientific papers (total in 7 papers)
Commutation Relations and Discrete Garnier Systems
Christopher M. Ormeroda, Eric M. Rainsb a University of Maine, Department of Mathemaitcs & Statistics, 5752 Neville Hall, Room 322, Orono, ME 04469, USA
b California Institute of Technology, Mathematics 253-37, Pasadena, CA 91125, USA
Abstract:
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlevé equations.
Keywords:
integrable systems; difference equations; Lax pairs; discrete isomonodromy.
Received: March 30, 2016; in final form October 30, 2016; Published online November 8, 2016
Citation:
Christopher M. Ormerod, Eric M. Rains, “Commutation Relations and Discrete Garnier Systems”, SIGMA, 12 (2016), 110, 50 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1192 https://www.mathnet.ru/eng/sigma/v12/p110
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Abstract page: | 154 | Full-text PDF : | 31 | References: | 31 |
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