Self-similarity, integrability, and accordions in transient stimulated Raman scattering

Abstract

Accordions, like their better-known mathematical cousins - soli tons - are similarity solutions of integrable partial differential equations. In the case of solitons, the similarity variable is x - νt} where x denotes position, t denotes time, and v denotes a velocity. In the case of accordions, the similarity variable is xtα. It can be shown that the solutions to the transient stimulated Raman scattering equations will always tend toward one of a two-parameter set of accordion solutions for any initial condition. The early history of these equations and related experiments is reviewed. The recent observation of accordions by the Russell group at the Max-Planck Institute for Light in Erlangen, Germany has rewoken interest in this topic and has suggested new mathematical work. Related work at Princeton that is aimed at applications to high-energy laser pulse generation will also be described.