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Kink-antikink interaction for semilinear wave equations with a small parameter. (English) Zbl 1173.35597

Summary: We consider a class of semilinear 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.

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B25 Singular perturbations in context of PDEs
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