Resonant interaction of ${\varphi }^4$ kink with spatially periodic $\mathcal{P}\mathcal{T}$-symmetric perturbation

Abstract

The resonant interaction of the ${\varphi }^4$ kink with a periodic $\mathcal{P}\mathcal{T}$-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.

10 pages, 10 figures

References in corpus (6)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Loss-induced suppression and revival of lasing
• Collective Coordinates in One-Dimensional Soliton Models Revisited
• Exact static solutions for discrete ${\varphi }^4$ models free of the Peierls-Nabarro barrier: Discretized first integral approach
• Interaction of sine-Gordon kinks and breathers with a $\mathcal{P}\mathcal{T}$-symmetric defect
• Radiationless energy exchange in three-soliton collisions

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• Asymmetric scattering between kinks and wobblers
• A new look at the double sine-Gordon kink-antikink scattering
• Scattering of the asymmetric ${\varphi }^6$ kinks from a $\mathcal{P}\mathcal{T}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons