The equations which describe stimulated Raman scattering in the transient limit are nonlinear and integrable. However, the physical behavior of this system after propagating, long distances is quite different from other integrable systems such as light pulses in optical fibers. In optical fibers, the light pulses break up into a number of solitons and a dispersive wave contribution, while in the transient regime of stimulated Raman scattering, the solutions tend toward a similarity solution which depends on (distance) x (time). This last result, while inferrable from previous numerical results, was only recently proved, and many of its consequences remain to be elucidated. The first issue of concern is the limitation which second Stokes generation and finite T2 impose on possible experimental observation of the self- similar solution. We will investigate this phenomenon. We will also explore the impact of the transient Raman effect on limiting the conversion efficiency of Raman frequency downshifters which are used in conjunction with Ti:Sapphire lasers. We will also explore the extent to which similar techniques can be applied to fiber gratings, two-level systems, photorefractive materials, and other systems which have either already been shown to exhibit self- similarity or are promising candidates because they have long-term memory. Finally, on the mathematical front, we will collaborate with Tom Seidman in studying the stability of these solutions and with other mathematicians in obtaining asymptotic formulae for the self-similar case when the frequencies are detuned.
