Resonant interaction of ϕ4 kink with PT-symmetric perturbation with spatially periodic gain/loss coefficient

Abstract

The resonant interaction of the φ 4 kink with a periodic 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 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.

Non-topological kink scattering in a two-component scalar field theory model

“…The exploration of this type of interactions must be carefully addressed and, nowadays constitutes a topic of significant interest [38,39,40,39,41,42,43,44,45,46]. The effect of defects, impurities or inhomogeneities on kink dynamics has been discussed in several models, see references [47,48,49,50,51,52,53,54,55,56,57,58]. The simultaneous collision of N kinks has also been recently studied for some of the previously mentioned systems, see [59,60,61].…”

Scattering between wobbling kinks

“…Kink dynamics has also been analyzed in coupled two-component scalar field theory models, see [42,43,44,45,46,47,48,49]. The effect of impurities, defects or inhomogeneities on kink dynamics has been discussed in several models, see references [50,51,52,53,54,55,56,57,58,59,60,61,62]. The previous description constitutes an heuristic explanation of the resonant energy transfer mechanism, although this phenomenon has revealed to be more complicated than expected.…”

Asymmetric kink scattering in a two-component scalar field theory model

“…An analytical explanation of this phenomenon is given in References [15,16,17]. The kink scattering together with the presence of the resonance windows have been explored in other models, such as in the double sine-Gordon model [18,19,20,21,22,23], in deformed φ 4 models [24,25,26,27], in φ 6 -models [28,29,30,31,32], in φ 8 -models [33,34,35], in models with defects, impurities or inhomogeneities [36,37,38,39,40,41,42,43,44], for the coupled nonlinear Schrodinger equations with vector solitons [45,46,47], etc. In these cases the resonant energy transfer mechanism is activated by the presence of vibrational modes of the single kinks or of a combined kink-antikink configuration.…”