UC hierarchy and monodromy preserving deformation

2010/07/20 by Teruhisa Tsuda, Tsuda, Teruhisa · 3 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1007.3450

Abstract

The UC hierarchy is an extension of the KP hierarchy, which possesses not only an infinite set of positive time evolutions but also that of negative ones. Through a similarity reduction we derive from the UC hierarchy a class of the Schlesinger systems including the Garnier system and the sixth Painleve equation, which describes the monodromy preserving deformations of Fuchsian linear differential equations with certain spectral types. We also present a unified formulation of the above Schlesinger systems as a canonical Hamiltonian system whose Hamiltonian functions are polynomials in the canonical variables.

Cited by

• Initial value space of the fourth order Painlevé system with A₅⁽¹⁾× A₁⁽¹⁾ symmetry
• Hypergeometric solution of a certain polynomial Hamiltonian system of isomonodromy type
• Hermite-Pade approximation, isomonodromic deformation and hypergeometric integral
• Tau functions of the UC hierarchy as partition functions of matrix models

Related

• Deformations of the Riemann hierarchy and the geometry of M_g,n
• Six-dimensional Painleve systems and their particular solutions in terms of hypergeometric functions
• Higher order Painleve system of type D⁽¹⁾_2n+2 and monodromy preserving deformation
• Restrictions on the existence of a canonical system flow hierarchy
• From KP/UC hierarchies to Painleve equations