ABSTRACT
This chapter discusses several applications of the dynamical projecting method (DPM) to problems of short pulse propagation in a dispersive medium. It focuses on two basic mathematical formulations: the Cauchy problem and boundary regime propagation along a waveguide. The DPM method is a convenient way to specify the problems of a wave initialization for directed modes and for a given polarization account. The chapter outlines an idea and implementation of the projection operators method that specify evolution operator subspaces. It presents an application of this approach to the derivation of a bidirectional wave system for hybrid elds. The chapter provides several applications of the projecting technique to cylindric waveguide modes and CNS-type equation derivation. It considers a dielectric cylindric waveguide with nonlinearities arising from third-order dielectric susceptibility. The account of nonlinear terms introduces into the physical picture the important phenomenon of mode interaction, which allows us to investigate energy and momentum transfer in a physically well-defined context.
