Diffraction effects on soliton propagation

Abstract

An averaged-Lagrangian method is used to analyze diffraction effects on propagation of solitons of various types in homogeneous media. It is shown that diffraction can counteract the self-focusing of dark and gray envelope solitons described by the nonlinear Schrodinger equation and solitons described by the Korteweg-de Vries equation when the soliton intensities do not exceed certain values. Conversely, diffraction enhances the self-focusing of dark and gray envelope solitons described by the modified Korteweg-de Vries equation, kinks described by the sine-Gordon equation, and domain walls in the u 4 model, which is explained by mutual correlation between transverse and longitudinal soliton dynamics. Critical parameters that determine soliton stability with respect to self-focusing are found for several models.