Electron. J. Diff. Eqns., Vol. 2009(2009), No. 45, pp. 1-26.

Kink-antikink interaction for semilinear wave equations with a small parameter

Martin G. Garcia, Georgii A. Omel'yanov

Abstract:
We consider a class of semi-linear wave equations with a small parameter and nonlinearities which provide the equations having exact kink-type solutions. As a main result we to obtain sufficient conditions for the nonlinearities under which the kink-antikink collision occurs without changing the waves shape and with only some shifts of the solitary wave trajectories.

Submitted October 28, 2008. Published March 30, 2009.
Math Subject Classifications: 35L70, 35L67, 35Q53.
Key Words: Semilinear wave equation; kink; antikink; interaction; distribution; asymptotic; weak asymptotic method.

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Martin G. Garcia
Universidad de Sonora, Mexico
email: mggarcia@gauss.mat.uson.mx
Georgii A. Omel'yanov
Universidad de Sonora, Mexico
email: omel@hades.mat.uson.mx

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