Degenerations of Ruijsenaars-van Diejen operator and q-Painleve equations

2016/08/31 by Kouichi Takemura · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Connection (principal bundle) #Differential equation #Geometry #Linear differential equation #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Pure mathematics #math-ph #math.CA #math.MP #math.QA #msc:33E10 #msc:33E17 #msc:39A13

paper · pdf · doi:10.1093/integr/xyx008

published as Journal of Integrable Systems, Volume 2, Issue 1, 2017, xyx008 · 28 pages, references added, minor revision

openalex created_date 2016/09/16 · openalex publication_date 2017/01/01 · arxiv created 2017/05/08 · arxiv updated 2018/01/26 · openalex updated_date 2026/08/05

Abstract

It is known that the Painleve VI is obtained by connection preserving deformation of some linear differential equations, and the Heun equation is obtained by a specialization of the linear differential equations. We inverstigate degenerations of the Ruijsenaars-van Diejen difference opearators and show difference analogues of the Painleve-Heun correspondence.

Citations

• Heun equation and Painlevé equation
• A q-anaolg of the sixth Painlevé equation
• Lax formalism for q-Painleve equations with affine Weyl group symmetry of type E⁽¹⁾_n

Cited by

• The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
• Heun function [wikipedia]

Related

• q-Heun equation and initial-value space of q-Painlevé equation
• Degenerations of q-Heun equation
• A q-analogue of the matrix fifth Painlevé system
• Classical transcendental solutions of the Painlevé equations and their degeneration
• New Coalescences for the Painlevé Equations