2018/05/31 by Katsushi Ito, Hongfei Shu
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Bethe ansatz #Black Holes and Theoretical Physics #Differential equation #Independent equation #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Monodromy #Nonlinear Waves and Solitons #Nonlinear system #Ode #Ordinary differential equation #Physics #Pure mathematics #Quantum mechanics #Toda lattice #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aad63f
1+26 pages, published version
openalex publication_date 2018/07/27 · arxiv created 2018/11/20 · arxiv updated 2018/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract The massive ordinary differential equation/integrable model (ODE/IM) correspondence is a relation between the linear problem associated with modified affine Toda field equations and 2D massive integrable models. We study the massive ODE/IM correspondence for the -type modified affine Toda field equations. Based on the ψ -system satisfied by the solutions of the linear problem, we derive the Bethe ansatz equations and determine the asymptotic behavior of the Q -functions for large values of the spectral parameter. We derive the non-linear integral equations for the Q -functions from the Bethe ansatz equations. We compute the effective central charge in the UV limit, which is identified by one of the non-unitary WA r minimal models when the solution has trivial monodromy around the origin of the complex plane.