32 citations · 33 across the 5 of their papers we have counts for
5 papers
On unconventional discretisations
Basil Grammaticos, Thamizharasi Tamizhmani, Ralph Willox
We present various discretisation techniques that mark a departure from the classical algorithms of numerical analysis, in the aim of preserving the physical behaviour of the solut…
Singularity interactions for lattice equations: introducing the taishi
Ralph Willox, Basil Grammaticos, Alfred Ramani +1
We study the singularities of some selected integrable lattice equations and show they all admit three types of singularities: one of finite and two of infinite extent. In particul…
On the singularity structure of a discrete modified-Korteweg-deVries equation
Basil Grammaticos, Thamizharasi Tamizhmani, Ralph Willox
We study the singularities of a modified lattice Korteweg-deVries (KdV) equation and show that it admits three families of singularities, with analogous properties to those found i…
Painlevé Analysis and Higher-Order Rogue Waves of a Generalized(3+1)-dimensional Shallow Water Wave Equation
Sudhir Singh, K. Sakkaravarthi, T. Tamizhmani +1
Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidi…
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…