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 …

We present a comprehensive review of the discrete Boussinesq equations based on their
three-component forms on an elementary quadrilateral. These equations were originally …

The pentagram map is a projectively natural transformation defined on (twisted) polygons. A
twisted polygon is a map from\mathbb Z into RP^ 2 that is periodic modulo a projective …

The usual Cauchy matrix approach starts from a known plain wave factor vector and known
dressed Cauchy matrix. In this paper, we start from a determining matrix equation set with …

A connection between the Yang-Baxter relation for maps and the multidimensional
consistency property of integrable equations on quad-graphs is investigated. The approach …

The direct linearization structure is presented of a “mild” but significant generalization of the
lattice BSQ system. Some of the equations in this system were recently discovered in [1] …

A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial
difference equations (PΔEs) is reviewed. The method assumes that the PΔEs are defined on …

In this paper an approach to generate multi-dimensionally consistent $ N $-component
systems is proposed. The approach starts from scalar multi-dimensionally consistent …

Various classes of one-component lattice equations, defined by a multi-linear relation
between values at the vertices of an elementary square, have recently been classified using …

The pentagram map is a discrete dynamical system defined on the moduli space of
polygons in the projective plane. This map has recently attracted a considerable interest …