30 citations · 213 across the 19 of their papers we have counts for
22 papers
Integrable and Chaotic 4-Dimensional Lotka-Volterra Models and Population Sustainability
H. Christodoulidi, T. E. Kouloukas, L. B. Drossos +1
We examine a 4-dimensional generalization of predator-prey models describing interactions among four species. We show that these systems exhibit a rich variety of asymptotic behavi…
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.
Deformations of cluster mutations and invariant presymplectic forms
Andrew N. W. Hone, Theodoros E. Kouloukas
We consider deformations of sequences of cluster mutations in finite type cluster algebras, which destroy the Laurent property but preserve the presymplectic structure defined by t…
Discrete Hirota reductions associated with the lattice KdV equation
Andrew N. W. Hone, Theodoros E. Kouloukas
We study the integrability of a family of birational maps obtained as reductions of the discrete Hirota equation, which are related to travelling wave solutions of the lattice KdV…
Cluster algebras and discrete integrability
Andrew N. W. Hone, Philipp Lampe, Theodoros E. Kouloukas
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and expl…
A new class of integrable Lotka-Volterra systems
H. Christodoulidi, A. N. W. Hone, T. E. Kouloukas
A parameter-dependent class of Hamiltonian (generalized) Lotka-Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cas…
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…
Relativistic Collisions as Yang-Baxter maps
Theodoros E. Kouloukas
We prove that one-dimensional elastic relativistic collisions satisfy the set-theoretical Yang-Baxter equation. The corresponding collision maps are symplectic and admit a Lax repr…
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…
Liouville integrability and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization
Theodoros E. Kouloukas, G. R. W. Quispel, Pol Vanhaecke
We prove the Liouville and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization.
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.
3D compatible ternary systems and Yang-Baxter maps
Theodoros E. Kouloukas, Vassilios G. Papageorgiou
According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps. After noticing that these…
Poisson Yang-Baxter maps with binomial Lax matrices
Theodoros E. Kouloukas, Vassilios G. Papageorgiou
A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped wi…
Entwining Yang-Baxter maps and integrable lattices
Theodoros E. Kouloukas, Vassilios G. Papageorgiou
Yang-Baxter (YB) map systems (or set-theoretic analoga of entwining YB structures) are presented. They admit zero curvature representations with spectral parameter depended Lax tri…
Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices
Theodoros E. Kouloukas, Vassilios G. Papageorgiou
A family of nonparametric Yang Baxter (YB) maps is constructed by refactorization of the product of two 2 by 2 matrix polynomials of first degree. These maps are Poisson with respe…