INTEGRABLE PARAMETER REGIMES AND STATIONARY STATES OF NONLINEARLY COUPLED ELECTROMAGNETIC AND ION-ACOUSTIC-WAVES

A systematic analysis of the stationary propagation of nonlinearly cou pled electromagnetic and ion-acoustic waves in an unmagnetized plasma via the ponderomotive force is carried out. For small but finite ampli tudes, the governing equations have a Hamiltonian structure, but with a kinetic energy term that is not positive definite. The Hamiltonian i s similar to the well-known Henon-Heiles Hamiltonian of nonlinear dyna mics, and is completely integrable in three regimes of the allowed par ameter space. The corresponding second invariants of motion are also e xplicitly obtained. The integrable parameter regimes correspond to sup ersonic values of the Mach number, which characterizes the propagation speed of the coupled waves. On the ether hand, in the sub-as well as near-sonic regimes, the coupled mode equations admit different types o f exact analytical solutions, which represent nonlinear localized eige nstates of the electromagnetic field trapped in the density cavity due to the ponderomotive potential. While the density cavity has always a single-dip structure, for larger amplitudes it can support higher-ord er modes having a larger number of nodes in the electromagnetic field. In particular, we show the existence of a new type of localized elect romagnetic wave whose field intensity has a triple-hump structure. For typical parameter values, the triple-hump solitons propagate with lar ger Mach numbers that are closer to the sonic limit than the single-as well as the double-hump solitons, but carry a lesser amount of the el ectromagnetic field energy. A comparison between the different types o f solutions is carried out. The possibility of the existence of trappe d electromagnetic modes having a larger number of humps is also discus sed. (C) 1998 American Institute of Physics.