64 citations · 239 across the 16 of their papers we have counts for
18 papers
The HANDY model with non-renewable resources and societal effects
Mathilde Badoual, Basil Grammaticos, Stéphane Plaszczynski +1
We present an extension of the single-population Human and Nature Dynamics (HANDY) model that explicitly incorporates non-renewable resources and societal effects. The model is for…
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…
Deautonomising the Lyness mapping
Basil Grammaticos, Alfred Ramani, Ralph Willox
We examine the Lyness mapping (an integrable th-order discrete system which can be generated from a one-dimensional reduction of the Hirota-Miwa equation) from the point of view…
The trouble with deautonomising higher order maps
Ralph Willox, Basil Grammaticos, Alfred Ramani
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity p…
A fast algorithmic way to calculate the degree growth of birational mappings
Basil Grammaticos, Alfred Ramani, Adrian Stefan Carstea +1
We present an algorithmic method for the calculation of the degrees of the iterates of birational mappings, based on Halburd's method for obtaining the degrees from the singularity…
Deautonomisation by singularity confinement and degree growth
Alexander Stokes, Takafumi Mase, Ralph Willox +1
In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement…
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…
Integrable mappings and the notion of anticonfinement
Takafumi Mase, Ralph Willox, Alfred Ramani +1
We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values co…
On the integrability of a new lattice equation found by multiple scale analysis
C. Scimiterna, M. Hay, D. Levi
In this paper we discuss the integrability properties of a nonlinear partial difference equation on the square obtained by the multiple scale integrability test from a class of mul…
Quantum Painlevé Equations: from Continuous to Discrete
Hajime Nagoya, Basil Grammaticos, Alfred Ramani
We examine quantum extensions of the continuous Painlevé equations, expressed as systems of first-order differential equations for non-commuting objects. We focus on the Painlevé e…
From Discrete to Continuous Painlevé Equations: A Bilinear Approach
Y. Ohta, A. Ramani, B. Grammaticos +1
We present the bilinear forms of the (continuous) Painlevé equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this m…
The Gambier Mapping
B. Grammaticos, A. Ramani
We propose a discrete form for an equation due to Gambier and which belongs to the class of the fifty second order equations that possess the Painleve property. In the continuous c…
Casorati Determinant Solutions for the Discrete Painlevé III Equation
Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma
The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are…
Integrable Trilinear PDE's
J. Hietarinta, B. Grammaticos, A. Ramani
In a recent publication we proposed an extension of Hirota's bilinear formalism to arbitrary multilinearities. The trilinear (and higher) operators were constructed from the requir…
Continuous vacua in bilinear soliton equations
J. Hietarinta, A. Ramani, B. Grammaticos
We discuss the freedom in the background field (vacuum) on top of which the solitons are built. If the Hirota bilinear form of a soliton equation is given by $A(D_{\vec x})\bd GF=0…
Linearization And Solutions Of The Discrete Painlevé-III Equation
B. Grammaticos, F. W. Nijhoff, V. Papageorgiou +1
We present particular solutions of the discrete Painlevé III (d-P) equation of rational and special function (Bessel) type. These solutions allow us to establish a close…
Casorati Determinant Solutions for the Discrete Painlevé-II Equation
Kenji Kajiwara, Yasuhiro Ohta, Junkichi Satsuma +2
We present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati…