Wobbling kinks in a two-component scalar field theory: Interaction between shape modes

TL;DR

This paper investigates the interaction between shape modes of wobbling kinks in a two-component scalar field theory, revealing complex mode couplings and radiation emission patterns through analytical and numerical methods.

Contribution

It uncovers the coupling dynamics between orthogonal and longitudinal shape modes in two-component kink models, with detailed analytical explanations of radiation frequencies.

Findings

Orthogonal mode excitation triggers longitudinal mode.

Kink emits radiation at frequencies related to wobbling modes.

Distinct radiation patterns in two components explained analytically.

Abstract

In this paper the interaction between the shape modes of the wobbling kinks arising in the family of two-component MSTB scalar field theory models is studied. The spectrum of the second order small kink fluctuation in this model has two localized vibrational modes associated to longitudinal and orthogonal fluctuations with respect to the kink orbit. It has been found that the excitation of the orthogonal shape mode immediately triggers the longitudinal one. In the first component channel the kink emits radiation with twice the orthogonal wobbling frequency (not the longitudinal one as happens in the $\phi^4$-model). The radiation emitted in the second component has two dominant frequencies: one is three times the frequency of the orthogonal wobbling mode and the other is the sum of the frequencies of the longitudinal and orthogonal vibration modes. This feature is explained analytically using perturbation expansion theories.