A unified framework is presented for the solution structure of three-dimensional discrete
integrable systems, including the lattice AKP, BKP and CKP equations. This is done through …

We study the Desargues maps, which generate lattices whose points are collinear with all
their nearest (in positive directions) neighbours. The multi-dimensional compatibility of the …

Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type
equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing …

We introduce integrable multicomponent non-commutative lattice systems, which can be
considered as analogues of the modified Gel'fand–Dikii hierarchy. We present the …

We discuss discretization of Koenigs nets (conjugate nets with equal Laplace invariants)
and of isothermic surfaces. Our discretization is based on the notion of dual quadrilaterals …

D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we
show that such a map provides solutions to the functional dynamical pentagon equation. We …

The C-quadrilateral lattice (CQL), also called the symmetric lattice, provides geometric
interpretation of the discrete CKP equation within the quadrilateral lattice (QL) theory. We …

We give an elaborated treatment of discrete isothermic surfaces and their analogues in
different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to …

S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the
thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduced …

The Sylvester equation plays an important role in many branches of mathematical physics.
The goal of this paper is to show that a special case of the Sylvester equation can be related …