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

Danial Saadatmand; Denis I. Borisov; Kun Zhou; Panayotis G. Kevrekidis; Sergey V. Dmitriev

Resonant interaction of φ⁴ kink with spatially periodic mathcal{PT}-symmetric perturbation

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arxiv 1611.08281 v1 pith:OZ7U2UGV submitted 2016-11-24 nlin.PS

Resonant interaction of φ⁴ kink with spatially periodic mathcal{PT}-symmetric perturbation

Danial Saadatmand , Denis I. Borisov , Panayotis G. Kevrekidis , Kun Zhou , Sergey V. Dmitriev This is my paper

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keywords kinkperturbationamplitudeinternalmodemodelresultscollective

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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.

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A resonance in phonons scattering off a kink in the absence of a Peierls-Nabarro potential
nlin.PS 2026-07 unverdicted novelty 6.0

In a Peierls-Nabarro-free discrete phi^4 model, phonon scattering off a kink exhibits lattice-spacing-dependent reflection and negative radiation pressure accelerating the kink toward incoming phonons due to resonances.