Resonant interaction of ϕ4 kink with [formula omitted]-symmetric perturbation with spatially periodic gain/loss coefficient

Abstract

The resonant interaction of the ϕ4 kink with a PT-symmetric perturbation is observed in the numerical study performed 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). The perturbation is in the form of first partial derivative in time term with a spatially periodic gain/loss coefficient. 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 the gain/loss prefactor in 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.