On reductions of some KdV-type systems and their link to the quartic   He'non-Heiles Hamiltonian
  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 quartic H\'enon-Heiles Hamiltonians. 
Caroline Verhoeven, Micheline Musette, and Robert Conte