Abstract
The present paper studies the interaction of Dirac δ-waves in models ruled by the nonlinear Klein-Gordon equation utt−c2uxx=ϕ(u), where c>0 is a real number and ϕ is an entire function taking real values on the real axis. Such study is made using a product of distributions that both extends the meaning of ϕ(u) for certain distributions u and allows the definition of a solution concept consistent with the classical solution concept. From such study, it emerges that in several nonlinear Klein-Gordon equations Dirac δ-waves behave like classical solitons in the sine-Gordon equation. As particular cases, this work examines the phi-four equation and the sine-Gordon equation.
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