This first introductory text to discrete integrable systems introduces key notions of
integrability from the vantage point of discrete systems, also making connections with the …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

A relationship between the tetrahedron equation for maps and the consistency property of
integrable discrete equations on Z 3 is investigated. Our approach is a generalization of a …

In this paper, we construct Yang–Baxter (YB) maps using Darboux matrices which are
invariant under the action of finite reduction groups. We present six-dimensional YB maps …

We construct birational maps that satisfy the parametric set-theoretical Yang–Baxter
equation and its entwining generalisation. For this purpose, we employ Darboux …

In this paper we show that there are explicit Yang–Baxter (YB) maps with Darboux–Lax
representation between Grassman extensions of algebraic varieties. Motivated by some …

Yang–Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang–Baxter
equation. For a set X= Ω× V, where V is a vector space and Ω is regarded as a space of …

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of
equations are presented. The class corresponds to a Lax operator with entries in a …

In this paper, we construct a Grassmann extension of a Yang-Baxter map which first
appeared in the work of Kouloukas and Papageorgiou [J. Phys. A: Math. Theor. 42, 404012 …

INTEGRABLE LATTICE MAPS: QV, A RATIONAL VERSION OF Q4 Page 1 Glasgow Math. J.
51A (2009) 157–163. C 2009 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089508004874 …