Space-Time Evolution of Nonlinear Three-Wave Interactions.

The space-time evolution is described in one dimension of the lowest order nonlinear interaction of three undamped wave packets. Dephasing effects due to inhomogeneity of the medium are included. An equivalent class of steady-state interactions in two dimensions is also described. The nonlinear saturation by pump depletion of instabilities which are absolute in the pump frame is found to involve only soliton transfer, thus allowing a complete solution in terms of an n-soliton formula. Energy transfer in both absolute and convective decay interactions in an inhomogeneous medium is found to plateau and then decrease with increasing pump width, in striking contrast to homogeneous interactions. The conclusions of the nonlinear analysis are applied to give a description of several nonlinear interactions of current interest in plasma physics. Depletion of a lower hybrid wave by decay to two other lower hybrid waves is calculated, and its possible effect on proposed schemes for radio frequency heating discussed.