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Interaction of kinks for semilinear wave equations with a small parameter. (English) Zbl 1096.35088

Summary: We consider a class of semilinear wave equations with a small parameter and nonlinearities such that the equations have exact kink-type solutions. The main result consists in obtaining sufficient conditions for the nonlinearities under which the interaction of kinks preserves the sine-Gordon scenario. This means that the interaction occurs without changing the waves shape and with shifts of trajectories.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35L67 Shocks and singularities for hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
35L15 Initial value problems for second-order hyperbolic equations
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