An Elliptic Garnier System

An Elliptic Garnier System We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at $${4m+12}$$ 4 m + 12 points for $${m \geq 1}$$ m ≥ 1 , which appear in pairs due to a symmetry condition. We parameterize this linear system in terms of a set of kernels at the singular points. We regard the system of discrete isomonodromic deformations as an elliptic analogue of the Garnier system. We identify the special case in which m = 1 with the elliptic Painlevé equation; hence, this work provides an explicit form and Lax pair for the elliptic Painlevé equation. Communications in Mathematical Physics Springer Journals

An Elliptic Garnier System

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag GmbH Germany
Physics; Theoretical, Mathematical and Computational Physics; Mathematical Physics; Quantum Physics; Complex Systems; Classical and Quantum Gravitation, Relativity Theory
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