Published May 8, 2017
| Version Submitted + Published
Journal Article
Open
A symmetric difference-differential Lax pair for Painlevé VI
Creators
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1.
University of Maine
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2.
California Institute of Technology
Abstract
We present a Lax pair for the sixth Painlevé equation arising as a continuous isomonodromic deformation of a system of linear difference equations with an additional symmetry structure. We call this a symmetric difference-differential Lax pair. We show how the discrete isomonodromic deformations of the associated linear problem gives us a discrete version of the fifth Painlevé equation. By considering degenerations, we obtain symmetric difference-differential Lax pairs for the fifth Painlevé equation and the various degenerate versions of the third Painlevé equation.
Additional Information
© 2017 The authors. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Received on 24 December 2016; editorial decision on 26 February 2017; accepted on 26 February 2017; Published: 08 May 2017. We would like to thank Frank Nijhoff for his correspondence and bringing our attention to [22], ER was supported by a grant from the National Science Foundation, [DMS-1500806]. We would also like to thank the anonymous referees for their diligence.Attached Files
Published - xyx003.pdf
Submitted - 1603.04393.pdf
Files
1603.04393.pdf
Additional details
Identifiers
- Eprint ID
- 83331
- Resolver ID
- CaltechAUTHORS:20171120-085000823
Related works
- Describes
- https://arxiv.org/abs/1603.04393 (URL)
Funding
- NSF
- DMS-1500806
Dates
- Created
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2017-11-20Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field
Caltech Custom Metadata
- Caltech groups
- Mathematics Department