30 citations · 213 across the 19 of their papers we have counts for
11 papers · 1 filter
Scalene Yang-Baxter maps and Lax triples
S. Konstantinou-Rizos, T. Kouloukas
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solut…
On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps
Pavlos Kassotakis, Theodoros E. Kouloukas, Maciej Nieszporski
We present rational Lax representations for one-component parametric quadrirational Yang-Baxter maps in both the abelian and non-abelian settings. We show that from the Lax matrice…
Reductions and degenerate limits of Yang-Baxter maps with Lax matrices
P. Adamopoulou, T. E. Kouloukas, G. Papamikos
We generalise a family of quadrirational parametric Yang-Baxter maps with Lax matrices by introducing additional essential parameters. These maps preserve a prescribed…
Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions
Pavlos Kassotakis, Theodoros Kouloukas, Maciej Nieszporski
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 colli…
Discrete integrable systems associated with relativistic collisions
Theodoros E. Kouloukas
We study vector quadrirational Yang-Baxter maps representing the momentum-energy transformation of two particles after elastic relativistic collisions. The collision maps admit Lax…
On non-abelian quadrirational Yang-Baxter maps
Pavlos Kassotakis, Theodoros Kouloukas
We introduce four lists of families of non-abelian quadrirational Yang-Baxter maps.
Some integrable maps and their Hirota bilinear forms
A. N. W. Hone, T. E. Kouloukas, G. R. W. Quispel
We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is s…
On Reductions of the Hirota-Miwa Equation
Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward
The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is inte…
A noncommutative discrete potential KdV lift
Sotiris Konstantinou-Rizos, Theodoros E. Kouloukas
In this paper, we construct a Grassmann extension of a Yang-Baxter map which first appeared in [16] and can be considered as a lift of the discrete potential Korteweg-de Vries (dpK…
Poisson structures for lifts and periodic reductions of integrable lattice equations
Theodoros E. Kouloukas, Dinh T. Tran
We introduce and study suitable Poisson structures for four dimensional maps derived as lifts and specific periodic reductions of integrable lattice equations. These maps are Poiss…
Integrable and superintegrable systems associated with multi-sums of products
Peter H. van der Kamp, Theodoros E. Kouloukas, G. R. W. Quispel +2
We construct and study certain Liouville integrable, superintegrable, and non-commutative integrable systems, which are associated with multi-sums of products.