An integrable hierarchy with a perturbed Hénon–Heiles system

@article{Hone2006AnIH,
  title={An integrable hierarchy with a perturbed H{\'e}non–Heiles system},
  author={Andrew N W Hone and V. G. Novikov and Caroline Verhoeven},
  journal={Inverse Problems},
  year={2006},
  volume={22},
  pages={2001 - 2020}
}
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 algebra method, we obtain the zero curvature representation of the equation, which leads to a Lax representation in terms of an energy-dependent Schrödinger spectral problem of the type studied by Antonowicz and Fordy. The solutions of this PDE system, and of its associated hierarchy of commuting flows, display weak… 
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