106 citations · 246 across the 12 of their papers we have counts for
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An integrable hierarchy with a perturbed Henon-Heiles system
A. N. W. Hone, V. S Novikov, C. Verhoeven
We consider an integrable scalar partial differential equation (PDE) that is second order in time. By rewriting it as a system and applying the Wahlquist-Estabrook prolongation alg…
Painleve' property of the He'non-Heiles Hamiltonians
Robert Conte, Micheline Musette, Caroline Verhoeven
Time independent Hamiltonians of the physical type H = (P_1^2+P_2^2)/2+V(Q_1,Q_2) pass the Painleve' test for only seven potentials , known as the He'non-Heiles Hamiltonians, ea…
Hamiltonians with two degrees of freedom admitting a singlevalued general solution
Robert Conte, Micheline Musette, Caroline Verhoeven
Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians whose some…
Completeness of the cubic and quartic Hénon-Heiles Hamiltonians
Robert Conte, Micheline Musette, Caroline Verhoeven
The quartic Hénon-Heiles Hamiltonian passes the Painlevé test for onl…
Explicit integration of the Hénon-Heiles Hamiltonians
Robert Conte, Micheline Musette, Caroline Verhoeven
We consider the cubic and quartic He'non-Heiles Hamiltonians with additional inverse square terms, which pass the Painleve' test for only seven sets of coefficients. For all the no…
On reductions of some KdV-type systems and their link to the quartic He'non-Heiles Hamiltonian
Caroline Verhoeven, Micheline Musette, Robert Conte
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and…