Ring wave solutions of a n+1-dimensional Sine-Gordon model

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (00, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.