Symmetry, Integrability and Geometry: Methods and Applications | |
The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I | |
关键词: q-Painlevé; Lax pairs; q-Schlesinger transformations; connection; isomonodromy; | |
DOI : | |
来源: DOAJ |
【 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