Type: Article

Scattering operator for nonlinear Klein-Gordon equations

Nakao Hayashi; Pavel I. Naumkin;

Abstract:

We prove the existence of the scattering operator in H(1+n/2,1) in the neighborhood of the origin for the nonlinear Klein-Gordon equation with a power nonlinearity u(tt) - Delta u + u = mu|u|(p-1)u, (t, x) is an element of R x R(n), where p > 1 + 2/n, mu is an element of C, n = 1, 2.