Henon-Heiles Hamiltonian for Coupled Upper-Hybrid and Magnetoacoutic Waves in Magnetized Plasmas

We show that the coupled mode equations for the stationary propagation of upper--hybrid and magnetoacoustic waves in magnetized electron--ion plasmas with negative group dispersion can be exactly derived from the generalized \Henon--Heiles Hamiltonian. The parameter regimes for the integrable cases of the coupled mode equations have been explicitly obtained. For positive group dispersion of the upper--hybrid waves, the relevant governing equations lead to a novel Hamiltonian where the kinetic energy is not positive definite.