Zobrazeno 1 - 10
of 50
pro vyhledávání: '"Kouloukas, Theodoros"'
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 equations turn out to be a particular case of these generic equat
Externí odkaz:
http://arxiv.org/abs/2412.03543
Autor:
Kouloukas, Theodoros E.
We study vector quadrirational Yang-Baxter maps representing the momentum-energy transformation of two particles after elastic relativistic collisions. The collision maps admit Lax representations compatible with an r-matrix Poisson structure and cor
Externí odkaz:
http://arxiv.org/abs/2305.06990
We introduce four lists of families of non-abelian quadrirational Yang-Baxter maps.
Comment: 13 pages, 1 figure. v2: Typos corrected
Comment: 13 pages, 1 figure. v2: Typos corrected
Externí odkaz:
http://arxiv.org/abs/2109.11975
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 the exchange matrix. The simplest example is the Lyness 5-cycle, arisin
Externí odkaz:
http://arxiv.org/abs/2107.11866
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 equation. In particular, for reductions corresponding to waves moving
Externí odkaz:
http://arxiv.org/abs/2003.08900
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 explain how discrete integrable systems can appear in the context of clust
Externí odkaz:
http://arxiv.org/abs/1903.08335
Autor:
Kouloukas, Theodoros E.
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 representation. Furthermore, they can be considered as reductions of a hig
Externí odkaz:
http://arxiv.org/abs/1706.06361
Publikováno v:
SIGMA 13 (2017), 057, 17 pages
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 integrable in the sense that it arises as the compatibility condition of a
Externí odkaz:
http://arxiv.org/abs/1705.01094
Publikováno v:
Journal of Mathematical Physics 59, 063506 (2018)
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 (dpKdV) equation. This noncommutative extension satisfies the Yang-Baxter
Externí odkaz:
http://arxiv.org/abs/1611.08923
We prove the Liouville and superintegrability of a generalized Lotka-Volterra system and its Kahan discretization.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/1601.05006