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Interaction of Solitons for Sine-Gordon-Type Equations

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  • Georgii A. Omel’yanov
  • Israel Segundo-Caballero

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.

Suggested Citation

  • Georgii A. Omel’yanov & Israel Segundo-Caballero, 2013. "Interaction of Solitons for Sine-Gordon-Type Equations," Journal of Mathematics, Hindawi, vol. 2013, pages 1-8, March.
    • Handle: RePEc:hin:jjmath:845926
    DOI: 10.1155/2013/845926
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