19 citations · 35 across the 5 of their papers we have counts for
6 papers
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…