Yaroslav Zolotaryuk

Discrete soliton ratchets driven by biharmonic fields.

Directed motion of topological solitons (kinks or antikinks) in the damped and ac-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the ac drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: nonzero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.

Discrete breathers in classical ferromagnetic lattices with easy-plane anisotropy.

Discrete breathers (nonlinear localized modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. This paper is devoted to the investigation of a classical d-dimensional ferromagnetic lattice with easy plane anisotropy. Its dynamics is described via the Heisenberg model. Discrete breathers exist in such a model and represent excitations with locally tilted magnetization. They possess energy thresholds and have no analogs in the continuum limit. We are going to review the previous results on such solutions and also to report new results. Among the new results we show the existence of a big variety of these breather solutions, depending on the respective orientation of the tilted spins. Floquet stability analysis has been used to classify the stable solutions depending on their spatial structure, their frequency, and other system parameters, such as exchange interaction and local (single-ion) anisotropy.

Directed motion of domain walls in biaxial ferromagnets under the influence of periodic external magnetic fields

AbstractnDirected motion of domain walls (DWs) in a classical biaxial ferromagnet placed under theninfluence of periodic unbiased external magnetic fields is investigated. Using the symmetry approachndeveloped in this article the necessary conditions for the directed DW motion are found. This motionnturns out to be possible if the magnetic field is applied along the easiest axis. The symmetrynapproach prohibits the directed DW motion if the magnetic field is applied along any of the hard axes.nWith the help of the soliton perturbation theory and numerical simulations, the average DW velocity as anfunction of different system parameters such as damping constant, amplitude, and frequency of the externalnfield, is computed.n

Moving Topological Solitons in the Discrete Klein-Gordon Equation

It is well known that (anti)kink propagation in Klein-Gordon lattices is hampered by the discreteness. However, depending on the shape of the on-site potential, a discrete set of velocities can appear, for which an (anti)kink can propagate freely. On several examples we show that this is a generic effect which takes place for potentials with rather flat barriers and narrow wells.

Moving Embedded Solitons in the Discrete Double Sine-Gordon Equation

The soliton mobility in the discrete double sine-Gordon (DDbSG) equation is investigated. This equation is used as a model of various physical applications, including the arrays of small Josephson junctions. In particular, it describes the array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) with one junction in one arm of the SQUID and two junctions in another arm of it. The DDbSG equation is investigated both in the hamiltonian limit and in the presence of dissipation and dc bias. The existence of perfectly localized embedded solitons that can propagate with some selected values of velocity has been demonstrated numerically with the help of the pseudo-spectral method. The embedded soliton existence diagram is constructed on the parameter plane. The signatures of the embedded solitons on the current-voltage curves of the array are discussed.

Nonlinear waves in a model for silicate layers

Some layered silicates are composed of positive ions, surrounded by layers of ions with opposite sign. Mica muscovite is a particularly interesting material, because there exist fossil and experimental evidence for nonlinear excitations transporting localized energy and charge along the cation rows within the potassium layers. This evidence suggests that there are different kinds of excitations with different energies and properties. Some of the authors proposed recently a one-dimensional model based on physical principles and the silicate structure. The main characteristic of the model is that it has a hard substrate potential and two different repulsion terms, between ions and nuclei. In a previous work with this model, it was found the propagation of crowdions, i.e., lattice kinks in a lattice with substrate potential that transport mass and charge. They have a single specific velocity and energy coherent with the experimental data. In the present work, we perform a much more thorough search for nonlinear excitations in the same model using the pseudospectral method to obtain exact nanopteron solutions, which are single kinks with tails, crowdions, and bi-crowdions. We analyze their velocities, energies, and stability or instability and the possible reasons for the latter. We relate the different excitations with their possible origin from recoils from different beta decays and with the fossil tracks. We explore the consequences of some variation of the physical parameters because their values are not perfectly known. Through a different method, we also have found stationary and moving breathers, that is, localized nonlinear excitations with an internal vibration. Moving breathers have small amplitude and energy, which is also coherent with the fossil evidence.

Embedded soliton dynamics in the asymmetric array of Josephson junctions

The dc-biased annular array of three-junction asymmetric superconducting quantum interference devices (SQUIDs) is investigated. The existence of embedded solitons (solitons that exist despite the resonance with the linear waves) is demonstrated both in the unbiased Hamiltonian limit and in the dc-biased and damped case on the current-voltage characteristics (CVCs) of the array. The existence diagram on the parameter plane is constructed. The signatures of the embedded solitons manifest themselves as inaccessible voltage intervals on the CVCs. The upper boundary of these intervals is proportional to the embedded soliton velocity.

Stability of Mode-Locked Kinks in the AC Driven and Damped Sine-Gordon Lattice

Kink dynamics in the underdamped and strongly discrete sine-Gordon lattice that is driven by the oscillating force is studied. The investigation is focused mostly on the properties of the mode-locked states in the overband case, when the driving frequency lies above the linear band. With the help of Floquet theory it is demonstrated that the destabilizing of the mode-locked state happens either through the Hopf bifurcation or through the tangential bifurcation. It is also observed that in the overband case the standing mode-locked kink state maintains its stability for the bias amplitudes that are by the order of magnitude larger than the amplitudes in the low-frequency case.

Radiation emission due to fluxon scattering on an inhomogeneity in a large two-dimensional Josephson junction

Interaction of a fluxon in the two-dimensional large Josephson junction with the finite-area inhomogeneity is studied within the sine-Gordon theory. The spectral density of the emitted plane waves is computed exactly for the rectangular and rhombic inhomogeneities. The total emitted energy as a function of the fluxon velocity exhibits at least one local maximum. Connection to the previously studied limiting cases including the point impurity and the one-dimensional limit has been performed. An important feature of the emitted energy as a function of the fluxon velocity is a clear maximum (or maxima). The dependence of these maxima on the geometric properties of the impurity has been studied in detail.

Scattering of quasi-one-dimensional solitons on impurities in large Josephson junctions

Abstract Fluxon transmission through impurities of different shape in a quasi-one-dimensional long Josephson junction is investigated. The junction width is significantly less than its length but, at the same time, is of the order of the Josephson penetration length λ J or exceeds it. The retrapping current on the impurities of the point, line and rectangular shape is computed as a function of the junction width both numerically and analytically. Good agreement between the analytic formulae and the numerical simulation results for the intermediate (several λ J ) junction width is observed.