Georgii A. Omel'yanov, Israel Segundo-Caballero
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. We declare sufficient conditions for
the nonlinearities under which the kink-kink and kink-antikink
collisions occur, in the asymptotic sense, without changing the
shape of the waves and with only some shifts of the solitary wave
trajectories. Furthermore, we create an absolutely stable finite
differences scheme to simulate the solution of the Cauchy problem
and obtain some numerical results for two-wave interaction. We
present also some unexpected results about three-wave
interaction.
Submitted April 16, 2010. Published October 21, 2010.
Math Subject Classifications: 35L71, 65M12, 35L67, 35Q53.
Key Words: Semilinear wave equation; kink; interaction;
asymptotic method; weak asymptotic method; finite differences scheme.
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Georgii A. Omel'yanov Universidad de Sonora, Mexico email: omel@hades.mat.uson.mx | |
Israel Segundo-Caballero Universidad de Sonora, Mexico email: segundo@gauss.mat.uson.mx |
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