Generation of wave packets and breathers by oscillating kinks in the sine-Gordon system

TL;DR

This paper investigates how oscillating kinks in the sine-Gordon system generate wave packets and breathers, revealing the dependence on initial conditions and spectral properties, with implications for understanding topological defect dynamics.

Contribution

It introduces a detailed analysis of oscillating sine-Gordon kinks and reformulates the scattering problem as a Schrödinger spectral problem to specify conditions for breather formation.

Findings

Oscillatory kink behavior depends on initial profile.

Wave packet and breather generation is linked to initial conditions.

Radiation energy depends on the initial profile's effective dimension.

Abstract

Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine-Gordon equation. The weakly damped oscillation of the sine-Gordon kink, named as the kink quasimode, is described explicitly. It is shown that the oscillatory kink behavior and the wave packet generation depend significantly on the initial nonequilibrium kink profile. In order to specify conditions of the generation of wobbling kinks with a multibreather structure we reformulate the direct scattering problem associated with the SG equation as the spectral problem of the Schr\"odinger operator. We obtain the dependence of the radiation energy, which is emitted during formation of the multi-frequency wobbling kink, on the effective dimension of its initial profile.