Low Temperature Physics: 47, 155 (2021); https://doi.org/10.1063/10.0003177
Fizika Nizkikh Temperatur: Volume 47, Number 2 (February 2021), p. 173-183    ( to contents , go back )

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

M. M. Bogdan1,2 and O. V. Charkina1

1B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of UkraineKharkiv 61103, Ukraine

2V. N. Karazin Kharkiv National University, Kharkiv 610022, Ukraine
E-mail: m_m_bogdan@ukr.net
charkina@ilt.kharkov.ua

pos Анотація:838

Received November 9, 2020, published online December 25, 2020

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 generationof 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 radiation energy, which is emitted during formation of the multi-frequency wobbling kink, on the effective dimension of its initial profile.

Key words: nonlinear dynamics, sine-Gordon equation, quasimode, wobbling kink, radiation.

Download 671710 byte View Contents