A Numerical Study of the Light Bullets Interaction in the (2+1) Sine-Gordon Equation

The propagation and interaction in more than one space dimension of localized pulse solutions (so-called light bullets) to the sine-Gordon SG] equation is studied both asymptotically and numerically. Similar solutions and their resemblance to solitons in integrable systems were observed numerically before in vector Maxwell systems. The simplicity of SG allows us to perform an asymptotic analysis of counterpropagating pulses, as well as a fully resolved computation over rectangular domains. Numerical experiments are carried out on single pulse propagation and on two pulse collision under different orientations. The particle nature, as known for solitons, persists in these two space dimensional solutions as long as the amplitudes of initial data range in a finite interval, similar to the conditions on the vector Maxwell systems.