Decay properties of periodic,radially symmetric solutions of Sine-Gordon-type equations

We investigate the radially symmetric, nonlinear wave equation and discuss the asymptotic behaviour as r → ∞ of solutions which are T-periodic in time t. It is shown that only two possibilities of decay can arise, namely polynomial like t^?½(n?1) and exponential e^?bt for some b > 0. Existence results are obtained.