Existence and stability of modulating pulse solutions in Maxwell’s equations describing nonlinear optics

AbstractModulating pulse solutions play a big rôle in modern long distance high speed communication. Such solutions consist of a traveling pulse-like envelope modulating an underlying electromagnetic wave. In this paper we show that under certain assumptions such solutions exist and are dynamically stable for the associated nonlinear partial differential equations, namely Maxwell’s integro-differential equations describing nonlinear optics. The analysis is worked out in detail for bulk media, and we discuss how the results extend to optical fibers and to parametrically forced systems.