INTEGRABILITY OF AN EXTENDED HENON-HEILES HAMILTONIAN FOR COUPLED NONLINEAR-WAVES

We consider an extension of the Henon-Heiles Hamiltonian to include hi gher order nonlinear as well as coupling terms which are relevant for coupled nonlinear wave propagations. It is shown that the resulting Ha miltonian, in its generic form, is integrable for two regimes in the p arameter space. The second integral of motion in each case is explicit ly obtained. Exact localized solutions of the relevant governing equat ions for the coupled waves corresponding to the two integrable cases o f the generic Hamiltonian are also given.