Resonant interaction of $\phi^4$ kink with spatially periodic $\mathcal{PT}$-symmetric perturbation

TL;DR

This paper investigates how a $ ext{phi}^4$ kink interacts resonantly with a spatially periodic $ ext{PT}$-symmetric perturbation, revealing quasiperiodic internal mode excitation and mode coupling effects that influence kink velocity.

Contribution

It introduces a collective variable model to analyze resonant kink interactions with $ ext{PT}$-symmetric perturbations, highlighting new dynamical features in open systems with balanced gain and loss.

Findings

Kink's internal mode amplitude grows quasiperiodically during resonance.

Kink velocity decreases as internal mode amplitude increases.

Qualitative agreement between collective variable model and numerical simulations.

Abstract

The resonant interaction of the $\phi^4$ kink with a periodic $\mathcal{PT}$-symmetric perturbation is observed in the frame of the continuum model and with the help of a two degree of freedom collective variable model derived in PRA 89, 010102(R). When the kink interacts with the perturbation, the kink's internal mode is excited with the amplitude varying in time quasiperiodically. The maximal value of the amplitude was found to grow when the kink velocity is such that it travels one period of perturbation is nearly one period of the kink's internal mode. It is also found that the kink's translational and vibrational modes are coupled in a way that an increase in the kink's internal mode amplitude results in a decrease in kink velocity. The results obtained with the collective variable method are in a good qualitative agreement with the numerical simulations for the continuum model. The results of the present study suggest that kink dynamics in open systems with balanced gain and loss can have new features in comparison with the case of conservative systems.