14 citations · 18 across the 4 of their papers we have counts for
4 papers
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…
A systematic approach to reductions of type-Q ABS equations
Mike Hay, Phil Howes, Nobutaka Nakazono +1
We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one particular reduction of Q3 is sho…
A Lax pair for the complete QRT mapping
P. Howes, N. Joshi, P. Kassotakis
QRT maps are translations on smooth biquadratic curves, also known as elliptic curves. Special cases of QRT maps are known to arise as compatibility conditions for an associated sy…
Global Asymptotics of the Second Painlevé Equation in Okamoto's Space
Phil Howes, Nalini Joshi
We study the solutions of the second Painlevé equation in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinit…