“Quantization” of an isomonodromic Hamiltonian Garnier system with two degrees of freedom

2015/04/30 by D. P. Novikov, B. I. Suleimanov
Mathematics · Physics and Astronomy · #Compatibility (geochemistry) #Differential equation #Hamiltonian (control theory) #Hamiltonian system #Integrable system #Linear differential equation #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1134/s0040577916040048

21 pages, in Russian

arxiv created 2015/06/24 · openalex publication_date 2016/04/01 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We construct solutions of analogues of a time-dependent Schrödinger equation corresponding to an isomonodromic polynomial Hamiltonian of a Garnier system with two degrees of freedom. The solutions are determined by solutions of linear differential equations whose compatibility condition is the given Garnier system. With explicit substitutions, these solutions reduce to solutions of the Belavin–Polyakov–Zamolodchikov equations with four times and two spatial variables.

Citations

• A relation between the Knizhnik--Zamolodchikov and Belavin--Polyakov--Zamolodchikov systems of partial differential equations
• Degeneration scheme of 4-dimensional Painlevé-type equations
• Classical conformal blocks and Painlevé VI