4 papers · 1 filter
On the singularities of the discrete Korteweg-deVries equation
Doyong Um, Alfred Ramani, Basil Grammaticos +2
We study the structure of singularities in the discrete Korteweg-deVries (d-KdV) equation. Four different types of singularities are identified. The first type corresponds to local…
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…
Restoring discrete Painlevé equations from an E-associated one
Basil Grammaticos, Alfred Ramani, Ralph Willox
We present a systematic method for the construction of discrete Painlevé equations. The method, dubbed `restoration', allows one to obtain all discrete Painlevé equations that shar…
Full-deautonomisation of a lattice equation
Ralph Willox, Takafumi Mase, Alfred Ramani +1
In this letter we report on the unexpected possibility of applying the full-deautonomisation approach we recently proposed for predicting the algebraic entropy of second-order bira…