91 citations · 187 across the 14 of their papers we have counts for
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Three-dimensional discrete systems of Hirota-Kimura type and deformed Lie-Poisson algebras
A. N. W. Hone, M. Petrera
Recently Hirota and Kimura presented a new discretization of the Euler top with several remarkable properties. In particular this discretization shares with the original continuous…
On the non-integrability of the Popowicz peakon system
Andrew N. W. Hone, Michael V. Irle
We consider a coupled system of Hamiltonian partial differential equations introduced by Popowicz, which has the appearance of a two-field coupling between the Camassa-Holm and Deg…
Algebraic curves, integer sequences and a discrete Painleve transcendent
A. N. W. Hone
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term bilinear recurrence relation of fourth order is given i…
Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
Alan K. Common, Andrew N. W. Hone
The Yablonskii-Vorob'ev polynomials , which are defined by a second order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They…
Integrable peakon equations with cubic nonlinearity
Andrew N. W. Hone, Jing Ping Wang
We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton…