Radial sine-Gordon kinks as sources of fast breathers

We consider radial sine-Gordon kinks in two, three, and higher dimensions. A full two-dimensional simulation showing that azimuthal perturbations remain small allows us to reduce the problem to the one-dimensional radial sine-Gordon equation. We solve this equation on an interval [r, r1] and absorb all outgoing radiation.

As the kink shrinks toward r, before the collision, its motion is well described by a simple law derived from the conservation of energy. In two dimensions for r ≤ 2, the collision disintegrates the kink into a fast breather, while for r ≥ 4 we obtain a kink-breather metastable state where breathers are shed at each kink “return.” In three and higher dimensions d, an additional kink-oscillon state appears for small r.

On the application side, the kink disintegration opens the way for new types of terahertz microwave generators.