Self-focusing in the perturbed and unperturbed nonlinear Schrodinger equation in critical dimension

A systematic perturbation theory for analyzing the effect of additional small terms on self-focusing is proposed, in which the perturbed critical nonlinear Schrodinger (NLS) equation is reduced to a simpler system of modulation equations that do not depend on the spatial variables transverse to the beam axis. The modulation equations can be further simplified, depending on whether the perturbed NLS is power conserving or not. Previous applications of modulation theory and present several new ones that include dispersive saturating nonlinearities, self-focusing with Debye relaxation, the Davey-Stewartson equations, self-focusing in optical fiber arrays, and the effect of randomness are presented.