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This paper is a continuation of our previous work Six-vertex model and non-linear differential equations I. Spectral problem in which we have put forward a method for studying the spectrum of the six-vertex model based on non-linear differential equations. Here we intend to elaborate on that approach and also discuss properties of the spectrum unveiled by the aforementioned differential formulation of the transfer matrixs eigenvalue problem. In particular, we intend to demonstrate how this differential approach allows one to study continuous symmetries of the transfer matrixs spectrum through the Lie groups method.
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The models partition function is shown to obey a system of PDEs resembling the celebrated Knizhnik-Zamol
We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanins separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of
To any differential system $dPsi=PhiPsi$ where $Psi$ belongs to a Lie group (a fiber of a principal bundle) and $Phi$ is a Lie algebra $mathfrak g$ valued 1-form on a Riemann surface $Sigma$, is associated an infinite sequence of correlators $W_n$ th
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically Mehlers kernel
We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and t