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 …

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 …

We show that integrable involutive maps, due to the fact they admit three integrals in
separated form, can give rise to equations, which are consistent around the cube and which …

Abstract The Hirota-Miwa equation (also known as the discrete KP equation, or the
octahedron recurrence) is a bilinear partial difference equation in three independent …

Integrable and superintegrable systems associated with multi-sums of products | Proceedings of
the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo Skip main …

In this letter we give fourth-order autonomous recurrence relations with two invariants,
whose degree growth is cubic or exponential. These examples contradict the common belief …

We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2,
and Q3 from the ABS list. The deautonomized form of one particular reduction of Q3 is …

The discrete-time Toda equation arises as a universal equation for the relevant Hankel
determinants associated with one-variable orthogonal polynomials through the mechanism …

We provide new examples of integrable rational maps in four dimensions with two rational
invariants, which have unexpected geometric properties, as for example orbits confined to …

We describe a method to obtain Lax pairs for periodic reductions of a rather general class of
integrable non-autonomous lattice equations. The method is applied to obtain reductions of …