126 citations · 722 across the 35 of their papers we have counts for
35 papers
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…
Special solutions of a discrete Painlevé equation for quantum minimal surfaces
Peter A. Clarkson, Anton Dzhamay, Andrew N. W. Hone +1
We consider solutions of a discrete Painlevé equation arising from a construction of quantum minimal surfaces by Arnlind, Hoppe and Kontsevich, and in earlier work of Cornalba and…
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…
Generalised higher-order Freud weights
Peter A. Clarkson, Kerstin Jordaan, Ana Loureiro
We discuss polynomials orthogonal with respect to a semi-classical generalised higher order Freud weight \[ω(x;t,λ)=|x|^{2λ+1}\exp\left(tx^2-x^{2m}\right),\qquad x\in\mathbb{R},\]…