29 citations · 287 across the 41 of their papers we have counts for
4 papers · 2 filters
On the singularity structure of the discrete KdV equation
Doyong Um, Ralph Willox, Basil Grammaticos +1
The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quad…
Discrete Painlevé equations from singularity patterns: the asymmetric trihomographic case
Basil Grammaticos, Alfred Ramani, Ralph Willox +1
We derive the discrete Painlevé equations associated to the affine Weyl group E that can be represented by an (in the QRT sense) "asymmetric" trihomographic system. The m…
Darboux dressing and undressing for the ultradiscrete KdV equation
Jonathan J. C. Nimmo, Claire R. Gilson, R. Willox
We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over for any potential with compact (finite) support, by explicitly con…
Constructing discrete Painlevé equations: from E to A and back
Alfred Ramani, Basil Grammaticos, Ralph Willox +1
The `restoration method' is a novel method we recently introduced for systematically deriving discrete Painlevé equations. In this method we start from a given Painlevé equation, t…