Transient Evolution, Stability for Disturbances, Multistability, and Chaos of Transverse Spatial Structures of a Lightwave Propagating in a Ring System with Inertial Nonlinear Medium

Abstract

In this paper we present our theoretical researches on shaping and stability of the transverse spatial radiation distribution in nonlinear systems. The analysis is based on constructing the Lyapunov functionals. We have determined the conditions for stable self-channelling of a light wave, its unlimited spreading, complication and chaos of transverse spatial distribution of radiation. It is demonstrated that a multithreshold self-channelling arises in nonlinear systems with several different focusing nonlinearities. The multistability phenomenon is discovered in the case of combination of focusing and defocusing nonlinea­rities.