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Journal of Mathematics
Volume 2013, Article ID 845926, 8 pages
http://dx.doi.org/10.1155/2013/845926
Research Article

Interaction of Solitons for Sine-Gordon-Type Equations

Department of Mathematics, University of Sonora, Rosales y Boulevard Encinas s/n, 83000 Hermosillo, Mexico

Received 27 November 2012; Accepted 23 January 2013

Academic Editor: Nasser Saad

Copyright © 2013 Georgii A. Omel’yanov and Israel Segundo-Caballero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions.