Theoretical investigations will be undertaken of nonlinear phenomena in plasmas and fluids. The four major areas of research will be: (1) Nonlinear effects on laser-plasma interactions, (2) solitons in optical wave guide systems, (3) algebraic structure of integrable nonlinear dynamical systems, and (4) control of plasma instability by neural networks. It is intended to study the effect of an induced smooth incoherent beam on nonlinear parametric instabilities, particularly the dramatic reduction of Raman backscattering. Analytic and numerical calculations will be performed of the distribution and emission rate of solitons from a resonant region as a function of pump power. Regimes will be identified in which regular propagation of steady solitons is possible in optical glass fibers. Attempts will be made to understand the mechanism that makes a nonlinear dynamical system integrable. Strategies will be investigated to feedback control macroscopic plasma instabilities through use of neural networks; a possible model system is a nonlinear multi- resonant electrical network with active elements.
