The Lattice Structure of Connection Preserving Deformations for q-Painlevé Equations I

Symmetry, Integrability and Geometry: Methods and Applications

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