Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Nieszporski, Maciej"'
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
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter maps, based
Externí odkaz:
http://arxiv.org/abs/1908.03019
We present two lists of multi-component systems of integrable difference equations defined on the edges of a $\mathbb{Z}^2$ graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimension
Externí odkaz:
http://arxiv.org/abs/1908.02413
Systems of difference equations on a vector valued function that admit 3D space of scalar potentials
For some involutive maps $\Phi:{\mathbb C}P^1 \times {\mathbb C}P^1 \to {\mathbb C}P^1 \times {\mathbb C}P^1$ we find all invariants with separated variables. We investigate a link of the maps and their invariants with separated variables to discrete
Externí odkaz:
http://arxiv.org/abs/1908.01706
Integrable discrete scalar equations defined on a~two or a three dimensional lattice can be rewritten as difference systems in bond variables or in face variables respectively. Both the difference systems in bond variables and the difference systems
Externí odkaz:
http://arxiv.org/abs/1710.11111
Publikováno v:
Proceedings: Mathematical, Physical and Engineering Sciences, 2020 Feb 01. 476(2234), 1-22.
Externí odkaz:
https://www.jstor.org/stable/26917953
We present a natural extension of the notion of nondegenerate rational maps (quadrirational maps) to arbitrary dimensions. We refer to these maps as $2^n-$rational maps. In this note we construct a rich family of $2^n-$rational maps. These maps by co
Externí odkaz:
http://arxiv.org/abs/1512.00771
Autor:
Atkinson, James, Nieszporski, Maciej
We give integrable quad equations which are multi-quadratic (degree-two) counterparts of the well-known multi-affine (degree-one) equations classified by Adler, Bobenko and Suris (ABS). These multi-quadratic equations define multi-valued evolution fr
Externí odkaz:
http://arxiv.org/abs/1204.0638
Publikováno v:
SIGMA 7 (2011), 100, 14 pages
We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund transformations. At least one of the members of each family is i
Externí odkaz:
http://arxiv.org/abs/1106.0636
We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2]. Lattice models
Externí odkaz:
http://arxiv.org/abs/1106.0435