The scattering theory for the nonlinear wave equation with small data (Q1084261)

A small data scattering problem for the nonlinear wave equation in \(R\times R^ n\), \(n=2,3,4,5\), is studied. The comparison between the asymptotics for \(t\to \pm \infty\) of the solutions of the nonlinear equation and the free wave equation is done in the standard Sobolev spaces \(H^{s,p}(R^ n)\) and \(\dot H^{s,p}(R^ n)\). This paper proposes a slight improvement in \(R^ 3\) and \(R^ 4\) of some previous results of John, Strauss and Klainerman.