DYNAMICS OF SOLITARY WAVES IN THE ZAKHAROV MODEL-EQUATIONS

We analyze internal vibrations of a solitary wave in the generalized Z akharov system (including a direct nonlinear self-interaction of the h igh-frequency field) by means of a variational approach. The applicati on of the variational approximation to this model turns out to be nont rivial, as one needs to renormalize the Lagrangian in order to avoid d ivergences. This is done with the use of two fundamental integrals of motion of the model. We derive a Hamiltonian two-degrees-of-freedom dy namical system that governs internal vibrations of the solitary wave. The eigenfrequencies of the small oscillations around the unperturbed solitary wave are found explicitly, one of them lying inside the gap o f the high-frequency subsystem, the other one being well above the gap . Finite-amplitude oscillations are simulated numerically. It is shown that these oscillations remain regular if the perturbation does not b reak the balance between the two integrals of motion, while in the opp osite case the oscillations are more irregular and may possibly become chaotic.