Wobbling kinks and shape mode interactions in a coupled two-component ${\varphi }^4$ theory

Abstract

The dynamics of a wobbling kink in a two-component coupled ${\varphi }^4$ scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in order to find the corresponding vibration modes associated to the first (longitudinal) and second (orthogonal) field components. By means of this analysis, it was found that the number of possible shape modes depends on the value of the coupling constant. It is notable that when one of the orthogonal field shape modes is initially triggered, the unique shape mode of the longitudinal field is also activated. This coupling causes the kink to emit radiation with twice the frequency of excited mode in the first field component. Meanwhile, in the orthogonal channel we find radiation with two different frequencies: one is three times the frequency of the orthogonal wobbling mode and another is the sum of the frequencies of the longitudinal shape mode and the triggered mode. All the analytical results obtained in this study have been successfully contrasted with those obtained through numerical simulations.

arXiv comment20 pages, 12 figures

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Cited by in corpus (3)

• Kink solutions in nonlocal scalar field theory models
• Localized structures in two-field systems: exact solutions in the presence of Lorentz symmetry breaking and explicit connection with geometric constraints
• Scattering between orthogonally wobbling kinks