  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.
