995 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Max Planck Institute for Radio AstronomyDE100 papers
- Centre National de la Recherche ScientifiqueFR91 papers
- Max Planck Institute for AstronomyDE76 papers
- University of EdinburghGB75 papers
- University of CambridgeGB74 papers
- University of LeedsGB69 papers
- Liverpool John Moores UniversityGB65 papers
- University of HertfordshireGB65 papers
- Imperial College LondonGB60 papers
- Rutherford Appleton LaboratoryGB52 papers
- University of OxfordGB50 papers
- Cardiff UniversityGB49 papers
67 papers · 1 filter
Discrete equations from Bäcklund transformations of the fifth Painlevé equation
Peter A. Clarkson, Clare Dunning, Ben Mitchell
In this paper discrete equations are derived from Bäcklund transformations of the fifth Painlevé equation, including a new discrete equation which has ternary symmetry. There are t…
Symmetric Sextic Freud Weight
Peter A. Clarkson, Kerstin Jordaan, Ana Loureiro
This paper investigates properties of the sequence of coefficients in the recurrence relation satisfied by the sequence of monic symmetric polynomials, orthogonal…
Integrable maps in 4D and modified Volterra lattices
A. N. W. Hone, J. A. G. Roberts, P. Vanhaecke +1
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperellipti…
Hamiltonian and recursion operators for a discrete analogue of the Kaup-Kupershmidt equation
Edoardo Peroni, Jing Ping Wang
In this paper we study the algebraic properties of a new integrable differential-difference equation. This equation can be seen as a deformation of the modified Narita-Itoh-Bogoyav…
Rational Solutions of the Fifth Painlevé Equation. Generalised Laguerre Polynomials
Peter A. Clarkson, Clare Dunning
In this paper rational solutions of the fifth Painlevé equation are discussed. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of…
Classical Solutions of the Degenerate Fifth Painlevé Equation
Peter A. Clarkson
In this paper classical solutions of the degenerate fifth Painlevé equation are classified, which include hierarchies of algebraic solutions and solutions expressible in terms of B…
Similarity reductions of peakon equations: integrable cubic equations
L. E. Barnes, A. N. W. Hone, M. Senthilvelan +1
We consider the scaling similarity solutions of two integrable cubically nonlinear partial differential equations (PDEs) that admit peaked soliton (peakon) solutions, namely the mo…
Quantisations of the Volterra hierarchy
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
In this paper we explore a recently emerged approach to the problem of quantisation based on the notion of quantisation ideals. We explicitly prove that the nonabelian Volterra tog…
Similarity reductions of peakon equations: the -family
Lucy E. Barnes, Andrew N. W. Hone
The -family is a one-parameter family of Hamiltonian partial differential equations of non-evolutionary type, which arises in shallow water wave theory. It admits a variety of s…
Perturbative Symmetry Approach for Differential-Difference Equations
A. V. Mikhailov, V. S. Novikov, J. P. Wang
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrab…
A Generalised Sextic Freud Weight
Peter A. Clarkson, Kerstin Jordaan
We discuss the recurrence coefficients of orthogonal polynomials with respect to a generalised sextic Freud weight \[ω(x;t,λ)=|x|^{2λ+1}\exp\left(-x^6+tx^2\right),\qquad x\in\mathb…
Linear relations for Laurent polynomials and lattice equations
Andrew N. W. Hone, Joe Pallister
A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. We consider a family of n…
Recursion and Hamiltonian operators for integrable nonabelian difference equations
Matteo Casati, Jing Ping Wang
In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. W…
Rational recursion operators for integrable differential-difference equations
Sylvain Carpentier, Alexander V. Mikhailov, Jing Ping Wang
In this paper we introduce preHamiltonian pairs of difference operators and study their connections with Nijenhuis operators and the existence of weakly non-local inverse recursion…
Some integrable maps and their Hirota bilinear forms
A. N. W. Hone, T. E. Kouloukas, G. R. W. Quispel
We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is s…
On Reductions of the Hirota-Miwa Equation
Andrew N. W. Hone, Theodoros E. Kouloukas, Chloe Ward
The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is inte…
Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
Allan P. Fordy, Pavlos Xenitidis
We recently introduced a class of graded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In particular, we introduce…
On Integrable Ermakov-Painlevé IV Systems
Colin Rogers, Andrew P. Bassom, Peter A. Clarkson
Novel hybrid Ermakov-Painlevé IV systems are introduced and an associated Ermakov invariant is used in establishing their integrability. Bäcklund transformations are then employed…
QRT maps and related Laurent systems
K. Hamad, A. N. W. Hone, P. H. van der Kamp +1
In recent work it was shown how recursive factorisation of certain QRT maps leads to Somos-4 and Somos-5 recurrences with periodic coefficients, and to a fifth-order recurrence wit…
Ermakov-Painlevé II Symmetry Reduction of a Korteweg Capillarity System
Colin Rogers, Peter A. Clarkson
A class of nonlinear Schrödinger equations involving a triad of power law terms together with a de Broglie-Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov-P…
Generalizations of the short pulse equation
Andrew N. W. Hone, Vladimir Novikov, Jing Ping Wang
We classify integrable scalar polynomial partial differential equations of second order generalizing the short pulse equation.
A noncommutative discrete potential KdV lift
Sotiris Konstantinou-Rizos, Theodoros E. Kouloukas
In this paper, we construct a Grassmann extension of a Yang-Baxter map which first appeared in [16] and can be considered as a lift of the discrete potential Korteweg-de Vries (dpK…
Conservation laws and integral relations for the Boussinesq equation
Adrian Ankiewicz, Andrew P. Bassom, Peter A. Clarkson +1
We are concerned with conservation laws and integral relations associated with rational solutions of the Boussinesq equation, a soliton equation solvable by inverse scattering whic…
Rational solutions of the Boussinesq equation and applications to rogue waves
Peter A. Clarkson, Ellen Dowie
We study rational solutions of the Boussinesq equation, which is a soliton equation solvable by the inverse scattering method. These rational solutions, which are algebraically dec…