We propose a specific class of matrices that participate in factorization problems that turn out
to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or …

In the recent years there is a growing interest in deriving and extending discrete integrable
systems to the non-abelian domain. At the same time there is an intrinsic connection of …

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

We extend the equations of motion that describe non-relativistic elastic collision of two
particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision …

We construct nocommutative set-theoretical solutions to the Yang–Baxter equation related to
the KdV, the NLS and the derivative NLS equations. In particular, we construct several Yang …

In this paper we revisit the Adler-Bobenko-Suris H2 equation. The H2 equation is linearly
related to the $ S^{(0, 0)} $ and $ S^{(1, 0)} $ variables in the Cauchy matrix scheme. We …

We study vector quadrirational Yang–Baxter maps representing the momentum–energy
transformation of two particles after elastic relativistic collisions. The collision maps admit …

We generalise a family of quadrirational parametric Yang-Baxter maps with $3\times 3$ Lax
matrices by introducing additional essential parameters. These maps preserve a prescribed …

It is shown how Yang–Baxter maps may be directly obtained from classical counterparts of
the star-triangle relations and quantum Yang–Baxter equations. This is based on …

There is a recently discovered formulation of the multidimensional consistency integrability
condition for lattice equations, called consistency-around-a-face-centered-cube (CAFCC) …