An extended Hénon-Heiles system

We consider an integrable system of partial differential equations possessing a Lax pair with an energy-dependent Lax operator of second order, of the type described by Antonowicz and Fordy. By taking the travelling wave reduction of this system we show that the integrable case (ii) Hénon-Heiles system can be extended by adding an arbitrary number of non-polynomial (rational) terms to the potential.