Self-similarity in stimulated Raman scattering

Abstract

The equations that govern stimulated Raman scattering in the transient limit have long been known to have soliton solutions, a Lax pair, and other properties that are normally associated with integrable systems. Yet the behavior of this system is known to be quite different from the usual behavior associated with integrable systems. Solitons are transient, and the behavior of the system at long distances is dominated by self-similarity. This behavior was first discovered numerically. In this presentation, we show that the self-similar solution can be derived by using symmetry reduction. We then show for fairly general initial conditions precisely which self-similar solution the system tends toward at long distances. These results are verified numerically. We argue that this behavior in which self-similar solutions dominate the longdistance evolution should often appear in nonlinear systems with memory. Finally, we outline an experiment that could observe the self-similar solutions.