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 consider 3D consistent six-tuples of quad-equations assigned to the faces of a cube. The
well-known classification of 3D consistent quad-equations, the so-called ABS-list, is …

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 …

We consider 3D consistent systems of six possibly different quad-equations assigned to the
faces of a cube. The well-known classification of 3D consistent quad-equations, the so …

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

We carry out the generalized symmetry classification of polylinear autonomous discrete
equations defined on the square, which belong to a twelve-parametric class. The direct …

We introduce a class of ${{\mathbb {Z}} _ {N}} $ graded discrete Lax pairs, with $ N\times N $
matrices, linear in the spectral parameter. We give a classification scheme for such Lax pairs …

We present an integrability test for discrete equations on the square lattice, which is based
on the existence of a generalized symmetry. We apply this test to a number of equations …

In this paper we prove that the trapezoidal $ H^{4} $ and the $ H^{6} $ families of quad-
equations are Darboux integrable by constructing their first integrals. This result explains …

In this work I discuss briefly the calculation of the algebraic entropy for systems of quad
equations. In particular, I observe that since systems of multilinear equations can have …