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

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 genera-tion 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 sine-Gordon equation as the spectral problem of the Schrödinger operator. We obtain the dependence of the radi-ation energy, which is emitted during formation of the multi-frequency wobbling kink, on the effective dimen-sion of its initial profile. © 2021 Institute for Low Temperature Physics and Engineering. All rights reserved.