26 citations · 116 across the 19 of their papers we have counts for
13 papers · 1 filter
A symmetric difference-differential Lax pair for Painlevé VI
Christopher M. Ormerod, Eric M. Rains
We present a Lax pair for the sixth Painlevé equation arising as a continuous isomonodromic deformation of a system of linear difference equations with an additional symmetry struc…
Commutation Relations and Discrete Garnier Systems
Christopher M. Ormerod, Eric M. Rains
We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems…
Spectral curves and discrete Painlevé equations
Christopher M. Ormerod
It is well known that isomonodromic deformations admit a Hamiltonian description. These Hamiltonians appear as coefficients of the characteristic equations of their Lax matrices, w…
From Polygons to Ultradiscrete Painlevé Equations
Christopher Michael Ormerod, Yasuhiko Yamada
The rays of tropical genus one curves are constrained in a way that defines a bounded polygon. When we relax this constraint, the resulting curves do not close, giving rise to a sy…
Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
Christopher M. Ormerod
We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlevé equation with symmetry. We prese…
Twisted reductions of integrable lattice equations, and their Lax representations
Christopher M. Ormerod, Peter H. van der Kamp, Jarmo Hietarinta +1
It is well known that from two-dimensional lattice equations one can derive one-dimensional lattice equations by imposing periodicity in some direction. In this paper we generalize…