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nlin.SI2012★ 4 cited
Multi-quadratic quad equations: integrable cases from a factorised-discriminant hypothesis
James Atkinson, Maciej Nieszporski
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 (…
nlin.SI2011★ 9 cited
Singularities of Type-Q ABS Equations
James Atkinson
The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable part…
nlin.SI2006
Seed and soliton solutions for Adler's lattice equation
James Atkinson, Jarmo Hietarinta, Frank Nijhoff
Adler's lattice equation has acquired the status of a master equation among 2D discrete integrable systems. In this paper we derive what we believe are the first explicit solutions…