Numerical study of a 'unique' sine-gordon 'breather' in (2+1) dimensions

摘要

We generalise previous numerical work of Evans, Cunha, Konotop and Vazquez~1 that utilised the Gear-Nordsieck~(2,3) predictor-corrector method to investigate solutions of the Sine-Gordon equation in (2+1) and (3+1) dimensions. We report, in particular a radially-lsymmetric "breather" solution in (2+1) dimensions that appears to have a unique amplitude and frequency. It does not "pulsate radially" and therefore appears distinct from other numerical solutions termed "pulsons" or "ring-solitions"~(4,5,6,7). Though found via a computation that assumed radial symmetry, the solution was later verified by simulating it in a "full" (2_1)-dimensional simulation. The simulations also show that small distortions to its shape did not lead to melchanical instability, which indicates its likely mechanical stability.