208 citations · 1.4k across the 68 of their papers we have counts for
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On a Schwarzian PDE associated with the KdV Hierarchy
Frank Nijhoff, Andrew Hone, Nalini Joshi
We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under Möbius transformations, that is related to the Korteweg-de V…
Discrete Dubrovin Equations and Separation of Variables for Discrete Systems
F. W. Nijhoff
A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of fi…
On the discrete and continuous Miura Chain associated with the Sixth Painlevé Equation
F. W. Nijhoff, N. Joshi, A. Hone
A Miura chain is a (closed) sequence of differential (or difference) equations that are related by Miura or Bäcklund transformations. We describe such a chain for the sixth Painlev…
On Discrete Painleve Equations Associated with the Lattice KdV Systems and the Painleve VI Equation
F. W. Nijhoff, A. Ramani, B. Grammaticos +1
A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painleve V equation. Its derivation is b…
Separation of variables for the Ruijsenaars system
V. B. Kuznetsov, F. W. Nijhoff, E. K. Sklyanin
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates ap…
Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
F. W. Nijhoff, V. B. Kuznetsov, E. K. Sklyanin +1
The classical r-matrix structure for the generic elliptic Ruijsenaars-Schneider model is presented. It makes the integrability of this model as well as of its discrete-time version…