Kink dynamics in spatially inhomogeneous media: the role of internal modes

Stability of bubble-like fluxons in disk-shaped Josephson junctions in the presence of a coaxial dipole current

We investigate analytically and numerically the stability of bubble-like fluxons in disk-shaped heterogeneous Josephson junctions. Using ring solitons as a model of bubble fluxons in the two-dimensional sine-Gordon equation, we show that the insertion of coaxial dipole currents prevents their collapse. We characterize the onset of instability by introducing a single parameter that couples the radius of the bubble fluxon with the properties of the injected current. For different combinations of parameters, we report the formation of stable oscillating bubbles, the emergence of internal modes, and bubble breakup due to internal mode instability. We show that the critical germ depends on the ratio between its radius and the steepness of the wall separating the different phases in the system. If the steepness of the wall is increased (decreased), the critical radius decreases (increases). Our theoretical findings are in good agreement with numerical simulations.

On the mechanical analogue of DNA

The creation of mechanical analogues of biological systems is known as a useful instrument that helps to understand better the dynamical mechanisms of the functioning of living organisms. Mechanical analogues of biomolecules are usually constructed for imitation of their internal mobility, which is one of the most important properties of the molecules. Among the different types of internal motions, angular oscillations of nitrous bases are of special interest because they make a substantial contribution to the base pairs opening that in turn is an important element of the process of the DNA-protein recognition. In this paper, we investigate the possibility to construct a mechanical analogue for imitation of angular oscillations of nitrous bases in inhomogeneous DNA. It is shown that the analogue has the form of a mechanical chain of non-identical pendulums that oscillate in the gravitational field of the Earth and coupled by identical springs. The masses and lengths of pendulums, as well as the distances between neighboring pendulums and the rigidity of springs are calculated. To illustrate the approach, we present the result of construction of the mechanical analogue of the fragment of the sequence of bacteriophage T7D.

Formation of a two-kink soliton pair in perturbed sine-Gordon models due to kink-internal-mode instabilities

The existence of two-kink soliton solutions in polynomial potentials was first reported by Bazeia et al. in a special type of scalar field systems [Phys. Rev. Lett. 91, 241601 (2003)]. A general feature of these potentials is that they possess two minima and a local metastable minimum between them. In the present work we investigate the appearance of this special kind of soliton in the sine-Gordon model under the perturbation of a space-dependent force. We show that a pair of solitons is emitted during the process of kink breakup by internal mode instabilities. A possible explanation of these phenomena is an interplay between the solitons repelling interaction and the external force, resulting in a separation or a packing of several kinks.

Spatiotemporal chaos in sine-Gordon systems subjected to wave fields: onset and suppression

The onset of spatiotemporal chaos in a damped sine-Gordon system subjected to a plane wave field as well as its suppression by an additional small-amplitude plane wave field are proposed theoretically and confirmed numerically. The relevance of these findings in the context of nonlinear magnetization waves is discussed.