Scattering of solutions for critical and subcritical nonlinear Klein-Gordon equations in \(H^s\) (Q1576872)

The author states two results on the existence of a scattering operator, from \(\{ (u,v)\in H^s\times H^{s-1} : (u,v)\) is small in \(H^r\times H^{r-1} \}\) for appropriate \(r\) and \(s\). The nonlinearity is power-like. This is a continuation of an earlier paper by the author [Nonlinear Anal., Theory Methods Appl. 31, No.~5-6, 573-587 (1998; Zbl 0886.35135)]. Proofs are only rapidly sketched; for instance, only wave operators are constructed, rather than the scattering operator.