Related papers: Resonantly driven wobbling kinks
The wobbling kink is the soliton of the $\phi^4$ model with an excited internal mode. We outline an asymptotic construction of this particle-like solution that takes into account the coexistence of several space and time scales. The…
We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behaviour of the radiation is described by matching the asymptotic expansions in the far field and near the…
In this paper the scattering between a wobbling kink and a wobbling antikink in the standard $\phi^4$ model is numerically investigated. The dependence of the final velocities, wobbling amplitudes and frequencies of the scattered kinks on…
The method of multiple scales is used to study the wobbling kink of the $\phi^4$ equation. The amplitude of the wobbling is shown to decay very slowly, as $t^{-1/2}$, and hence the wobbler turns out to be an extremely long-lived object.
The dynamics of a wobbling kink in a two-component coupled $\phi^4$ scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in…
We study the dynamics of kinks in the $\phi^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the…
We study the collision of a kink and an antikink in the double sine-Gordon model with and without the excited vibrational mode. In the latter case, we find that there is a limited range of the parameters where the resonance windows exist,…
We study the dynamics of $\phi^4$ kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
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,…
The dynamical backaction from a periodically driven optical or microwave cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Fundamentally, the driving…
The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions…
The radiation from oscillating kink in (1+1) dimensional relativistic $\phi^4$ model is considered. Both analytical and numerical approaches are presented and the comparison between these methods is discussed. Acceleration of the kink in…
The asymmetric scattering between wobblers and kinks in the standard $\phi^4$ model is numerically investigated in two different scenarios. First, the collision between wobblers with opposite phase is analyzed. Here, a destructive…
In this paper the interaction between the shape modes of the wobbling kinks arising in the family of two-component MSTB scalar field theory models is studied. The spectrum of the second order small kink fluctuation in this model has two…
We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $\Omega_i$. We show that the strongest resonance arises when the driving frequency $\delta=\Omega_i/2$,…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
Near-resonant ac-drive acting on a two-level system induces the Rabi oscillations of the level occupations. It is shown that additional weak drive properly frequency-detuned from the primary drive causes a resonant response. This response…
Dynamics of sine-Gordon kinks in the presence of rapidly varying periodic perturbations of different physical origins is described analytically and numerically. The analytical approach is based on asymptotic expansions, and it allows to…