Symmetry Integrability and Geometry-Methods and Applications | |
The Lattice Structure of Connection Preserving Deformations for q -Painlevé Equations I | |
article | |
Christopher M. Ormerod1  | |
[1] La Trobe University, Department of Mathematics and Statistics | |
关键词: q-Painlev´e; Lax pairs; q-Schlesinger transformations; connection; isomonodromy; | |
DOI : 10.3842/SIGMA.2011.045 | |
来源: National Academy of Science of Ukraine | |
【 摘 要 】
We wish to explore a link between the Lax integrability of the q -Painlevé equations and the symmetries of the q -Painlevé equations. We shall demonstrate that the connection preserving deformations that give rise to the q -Painlevé equations may be thought of as elements of the groups of Schlesinger transformations of their associated linear problems. These groups admit a very natural lattice structure. Each Schlesinger transformation induces a Bäcklund transformation of the q -Painlevé equation. Each translational Bäcklund transformation may be lifted to the level of the associated linear problem, effectively showing that each translational Bäcklund transformation admits a Lax pair. We will demonstrate this framework for the q -Painlevé equations up to and including q -P VI .
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO202106300001660ZK.pdf | 428KB | download |