  Radiation field and channel of energy method have become important tools in
the study of nonlinear wave equations in recent years. In this work we give
basic theory of radiation fields of free waves in the energy sub-critical case.
We also show that the asymptotic behaviours of non-radiative solutions to a
wide range of non-linear wave equations resemble those of non-radiative free
waves. Our theory is completely given in the critical Sobolev spaces of the
corresponding nonlinear wave equation and avoids any assumption on the energy
of the solutions.
