Generalized wave operators for a system of nonlinear wave equations in three space dimensions

This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically symmetric,we shall show global solvability of the final value problem around a suitable final state, and hence the generalized wave operator and long range scattering operator can be constructed.