Radial sine-Gordon kinks as sources of fast breathers

TL;DR

This paper investigates radial sine-Gordon kinks in multiple dimensions, showing how they disintegrate into breathers or form metastable states, with potential applications in terahertz microwave generation.

Contribution

It introduces a reduced one-dimensional model for radial sine-Gordon kinks in higher dimensions and characterizes their collision outcomes and states across parameters.

Findings

Kinks disintegrate into breathers in 2D for small r0.

Kinks form kink-breather metastable states for larger r0.

Kink-pulson states appear in higher dimensions.

Abstract

We consider radial sine-Gordon kinks in two, three and higher dimensions. A full two dimensional simulation showing that azimuthal perturbations remain small allows to reduce the problem to the one dimensional radial sine-Gordon equation. We solve this equation on an interval $[r_0,r_1]$ and absorb all outgoing radiation. Before collision the kink is well described by a simple law derived from the conservation of energy. In two dimensions for $r_0 \le 2$, the collision disintegrates the kink into a fast breather while for $r_0 \ge 4$ we obtain a kink-breather meta-stable state where breathers are shed at each kink "return". In three and higher dimensions $d$ a kink-pulson state appears for small $r_0$. The three states then exist as shown by a study of the $(d,r_0)$ parameter space. On the application side, the kink disintegration opens the way for new types of terahertz microwave generators.