91 citations · 187 across the 14 of their papers we have counts for
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Tau-functions and special solutions in a coupled Painlevé system
A. N. W. Hone
For a pair of coupled Painlevé equations obtained as a similarity reduction of the Hirota-Satsuma systems we describe special parameter-families of solutions given in terms of mixt…
O(n) invariant solutions of Abreu's equation
A. N. W. Hone
We consider a fourth order partial differential equation in n-dimensional space introduced by Abreu in the context of Kähler metrics on toric orbifolds. Similarity solutions depend…
On the non-integrability of a fifth order equation with integrable two-body dynamics
D. D. Holm, A. N. W. Hone
We consider the fifth order partial differential equation (PDE) , which is a generalization of the integrab…
A New Integrable Equation with Peakon Solutions
A. Degasperis, D. D. Holm, A. N. W. Hone
We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the…