Nonlinear small data scattering for the wave equation in \(\mathbb{R}^{4+1}\) (Q1127663)

The paper deals with a small solution of the semilinear wave equation \[ \partial^2_tu- \Delta u=\lambda|u|^{p-1}u \] with the four-dimensional space variable \(x\). The main result is an existence theorem of the global solution of the Cauchy problem in the case \(p>2\). An asymptotics of the solutions as \(t\to\pm\infty\) is obtained and the scattering operator is defined as well.