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 (0</= varepsilon <<1,0</=alpha<<1) are studied analytically and numerically for spatial dimension (n=2,3). The model is obtained as a continuum approximation of a multidimensional Frenkel-Kontorowa lattice. We will show that in the case varepsilon >0, 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.