QUALITATIVE-ANALYSIS OF RADIATING BREATHERS

Perturbed sine-Gordon equations are investigated numerically to see if they have breather solutions. It is shown that breathers radiate, blow up, and split into kink-antikink pairs under most perturbations. The two perturbations proven by Birnir, McKean, and Weinstein not to produce radiation, of the first order in the perturbation parameter, a sin(u) + b ucos(u) and 1 + 3cos(u) - 4cos(u/2) + 4cos(u)log(cos(u/4)), stop radiating first-order radiation after adjusting the initial breather by the emission of such radiation. The first perturbation is a scaling of the breather, the second is shown to give a quasi-periodic orbit, which is a two-breather, on a torus. (C) 1994 John Wiley & Sons, Inc.