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 Schrödinger 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.
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 125, No. 6, 2004, pp. 1409–1422.
Original Russian Text Copyright © 2004 by Sazonov.
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Sazonov, S.V. Diffraction effects on soliton propagation. J. Exp. Theor. Phys. 98, 1237–1249 (2004). https://doi.org/10.1134/1.1777637
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DOI: https://doi.org/10.1134/1.1777637