110 citations · 452 across the 18 of their papers we have counts for
20 papers
Suleimanov-Talanov self-focusing and the hierarchy of the focusing nonlinear Schrödinger equation
Robert J. Buckingham, Robert M. Jenkins, Peter D. Miller
We study the self-focusing of wave packets from the point of view of the semiclassical focusing nonlinear Schrödinger equation. A type of finite-time collapse/blowup of the solutio…
Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III Equation
Robert J. Buckingham, Peter D. Miller
It is well known that the Painlevé equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits. A way to make…
On the algebraic solutions of the Painleve-III (D7) equation
Robert J. Buckingham, Peter D. Miller
The D7 degeneration of the Painleve-III equation has solutions that are rational functions of for certain parameter values. We apply the isomonodromy method to obtain a R…
Large-degree asymptotics of rational Painleve-IV solutions by the isomonodromy method
Robert J. Buckingham, Peter D. Miller
The Painleve-IV equation has two families of rational solutions generated respectively by the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply the…
Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit
Deniz Bilman, Robert Buckingham, Deng-Shan Wang
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We st…
A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
Estelle Basor, Pavel Bleher, Robert Buckingham +4
We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the sigma-Painleve V equatio…