149 citations · 351 across the 16 of their papers we have counts for
16 papers
Quadrirational Yang-Baxter maps and the elliptic Cremona system
James Atkinson, Yasuhiko Yamada
This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analo…
Coble's group and the integrability of the Gosset-Elte polytopes and tessellations
James Atkinson
This paper considers the planar figure of a combinatorial polytope or tessellation identified by the Coxeter symbol , inscribed in a conic, satisfying the geometric const…
Geometry of an elliptic-difference equation related to Q4
James Atkinson, Phil Howes, Nalini Joshi +1
In this paper, we investigate a nonlinear non-autonomous elliptic difference equation, which was constructed by Ramani, Carstea and Grammaticos by integrable deautonomization of a…
On the lattice-geometry and birational group of the six-point multi-ratio equation
James Atkinson
The inherent self-consistency properties of the six-point multi-ratio equation allow it to be considered on a domain associated with a T-shaped Coxeter-Dynkin diagram. This extends…
Quadrirational Yang-Baxter maps and the affine-E8 Painleve lattice
James Atkinson, Yasuhiko Yamada
We establish that the quadrirational Yang-Baxter maps, considered on their symmetry-complete lattice, give an un-normalized form of the Painleve systems associated with affine-E8 s…
Idempotent biquadratics, Yang-Baxter maps and birational representations of Coxeter groups
James Atkinson
A transformation is obtained which completes the unification of quadrirational Yang-Baxter maps and known integrable multi-quadratic quad equations. By combining theory from these…