Diffraction effects on soliton propagation

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. (C) 2004 MAIK "Nauka / Interperiodica".