Search

We extend the constant-variation method to the case of partial differential equations. Applying the method to periodically perturbed Sine-Gordon system, we find some novel solitons, which are embedded in a chaotic attractor and possess controllable velocity of motion. Taking periodically driven long Josephson junction as an example the corresponding chaotic region in parameter space and chaotic orbit are obtained analytically and numerically.

We have recorded the radiation generated by magnetic flux quanta oscillations and by cavity mode oscillations in two-stacked arrays each consisting of five long Josephson junctions biased in parallel. The two arrays have in common the middle electrode, which is thinner than the London penetration depth, and can be biased independently. Basically, two kind of fluxon states can be generated, one consisting of a row of five fluxons oscillating in one of the arrays, the other consisting of a row of five fluxons in one array and five antifluxons in the other array, bound in a coherent state. It is found from the microwave emission that the latter configuration is less sensitive to low-frequency noise.

Stability of Josephson junction clock sources can be a limiting factor in the operation of RSFQ digital and mixed signal circuits. We have developed techniques for the characterization of the short-term stability, i.e., the jitter, of Josephson junction clock sources, and in this paper we present measurements of the jitter for a long Josephson junction soliton oscillator clock. The output frequency of the soliton oscillator was prescaled by using a chain of T flip-flops and using a current bias feedback the oscillator was phase locked to a stable room temperature RP source. Phase noise spectra of the clock signal were measured at the successive stages of the T flip-flop chain and interpreted to infer the cycle-to-cycle jitter of the soliton oscillator. The jitter at the output of the soliton oscillator was measured to be 60 fs at a frequency of 26 GHz, or 0.16% of the period of the clock.

The Josephson Flux Flow Oscillator (FFO) has proven to be a perfect on-chip local oscillator for integrated submm receivers; a noise temperature (DSB) below 100 K has been achieved at 500 GHz. Recently a FFO linewidth as low as 1 Hz has been measured in the frequency range 270 - 440 GHz. A new technique for both linewidth measurements and phase locking of the FFO is developed; this method employs an offchip harmonic multiplier. By measuring the frequency of the FFO radiation emission, its IV-curve (IVC) can be reconstructed with an accuracy better than 1 nV. A superfine resonant structure with a voltage spacing of about 20 nV and extremely low differential resistance has been observed in the FFO IVCs. This resonant structure modifies the performance of the FFO compared to the one expected from the "averaged IVC". The influence of this resonant structure on phase locking is discussed. Also results of FFO phase noise measurements are presented.

A novel Cherenkov flux flow oscillator (CFFO) is considered. The system consists of a long Josephson junction with an overlaying meander-shaped stripline. The traveling wave in the line is exited at each intersection point by the chain of fluxons moving along the junction. At certain resonance frequencies the radiation delivered to the stripline from all intersections points interfere constructively and the generated power reaches its maximum value. To first order the resonance condition is given by the distance between the fluxons, and is independent of the system boundaries. So one can change the resonance frequency by varying the external magnetic field. This is radically different from oscillators relying on conventional internal junction resonances such as the Fiske resonance, and allows for design of a powerful CFFO which can be electronically tuned. The existence of resonant interactions with both forward and backward waves is shown, and the analogy to the Cherenkov synchronism is demonstrated. Numerical simulations confirm the analytical predictions and allow us to investigate the strongly nonlinear case. The proposed CFFO is ideally suited for realization in HTSC technology.

The dependence of the first critical field of long linear and annular Josephson junctions on the width of the surrounding stripline, the so called idle region, is investigated experimentally. The stripline modifies the effective Josephson length λeff in the junction. The experimental data are compared with the theory by Caputo et al. [J. Appl. Phys. 85, 7291 (1999)] and good agreement is found. The dependence of the first critical field on the width of the surrounding stripline can be well explained using the same λeff for both annular and linear junctions.

Kinks and rotations are studied in long Josephson junctions for small and large surface losses. Geometric singular perturbation theory is used to prove existence for small surface losses, while numerical continuation is necessary to handle large surface losses. A survey of the system behaviour in terms of dissipation parameters and bias current is given. Linear orbital stability for kinks is proved for small surface losses by calculating the spectrum of the linearized problem. The spectrum is split into essential spectrum and discrete spectrum. For the determination of the discrete spectrum, robustness of exponential dichotomies is used. Puiseux series together with perturbation theory for linear operators are an essential tool. In a final step, a smooth Evans function together with geometric singular perturbation theory is used to count eigenvalues. For kinks, non-linear orbital stability is shown. For this purpose, the asymptotic behaviour of a semigroup is given and the theory of centre and stable manifolds is applied. Copyright © 2001 John Wiley & Sons, Ltd.

A collective coordinate approach is applied to study chaotic responses induced by an applied biharmonic driven signal on the long Josephson junction influenced by a constant dc-driven field with breather initial conditions. We derive a nonlinear equation for the collective variable of the breather and a new version of the Melnikov method is then used to demonstrate the existence of Smale horseshoe-shaped maps in its dynamics. Additionally, numerical simulations show that the theoretical predictions are well reproduced. The subharmonic Melnikov theory is applied to study the resonant breathers. Results obtained using this approach are in good agreement with numerical simulations of the dynamics of the Poincare islands.

The first analytical description of the 4 π -kink Josephson vortex is presented for the model of the long Josephson junction with the sine-nonlinearity. The weakly nonlocal approach is used. This approach is efficient for the description of the vortices moving with the velocities which are close to the Swihart velocity. This new analytical result is obtained in the limit when the Josephson critical current density is not high enough.

We present a review of the dynamical states of the long Josephson junction when dc and ac currents are considered as bias terms. When only the dc terms are present, depending on the value of the external magnetic field, the excitations consists of fluxon oscillations, cavity modes and travelling waves interactions with the Josephson effect. These three different modes generate well identified singularities in the current-voltage characteristics. We also report on the effect that ac current terms applied to the transmission line can have on these current singularities. In this case a theoretical analysis, based on the nature of dc excitations, has provided predictions for the ranges of locking of the external signal to junction’s oscillations. These predictions are in good agreement with experimental and numerical data that have been reported in the literature.

The Josephson Flux-Flow Oscillator (FFO) has been used as an on chip local oscillator at frequencies up to 650 GHz. The FFO linewidth of about 1 MHz was measured in the resonant regime at V

This paper is devoted to the experimental investigation of a new class of superconducting microwave oscillators based on Cherenkov radiation from Josephson vortices. Samples consisting of a long Josephson junction embedded in a dispersive transmission line with space-periodical inhomogeneities were fabricated and tested. We report observation of new resonances on the I-V curve of the system and present the first radiation measurements in the 80-120 GHz frequency range.

In the hypothesis that good quality high temperature superconducting (HTS) films can be modeled as an agglomeration of islands coupled via Josephson contacts, we calculate the critical current density J/sub c/ vs. field in a long Josephson junction (LJJ). The coupling energies in the junction are modulated by defects with given distribution and size. The superconductor is then considered as a network of LJJ between superconducting islands. Each LJJ has a different defect distribution. The model accounts for all main trends of the experimental electromagnetic behavior. The most important issue is that a "hidden" network of LJJ with a suitable distribution of optimized defects is the source of high critical current density in "good quality" films. Therefore any needed response of the film in a given range of field can be designed in advance.

By combining a long Josephson junction (LJJ) with single-flux-quantum (SFQ) circuits, new digital applications for long junctions can be explored. To fully investigate the dynamics of the hybrid LJJ/SFQ circuits, a numerical model was developed for an unshunted long junction coupled to shunted SFQ Josephson transmission line (JTL) through superconducting strips. The model is based on a one-dimensional array of Josephson junctions that is described by a set of discrete sine-Gordon equations. Simulations support our experimental observation that the first zero-field step can exist when the LJJ is terminated by SFQ elements. The influences on the first zero-field step by the self-inductance, the critical current, and the shunt resistance of JTL cells are studied in detail. Simulation also confirms that each 4/spl pi/ phase leap at the end of the long junction creates two separated SFQ pulses after several overdamped JTL cells.

Resistive branches have often been observed in the current-voltage characteristics of long Josephson junctions. In the present paper we perform a systematic numerical analysis of the generation of these branches when an external magnetic field is applied to the junctions. We show that the linear branches exist only over a limited voltage interval which is determined quantitatively. We also clarify to what extent the linear branches can be attributed to flux-flow effects.

It is shown that there are two vortex states for the configuration of an Abrikosov vortex in the presence of a long Josephson junction. One state, dubbed `conventional', carries one magnetic-flux quantum Φ 0 , as does the generating Abrikosov vortex. The second and new vortex state entails in addition to the generating vortex two Josephson vortices with opposite polarity to that of the generating-vortex and its magnetic flux is − Φ 0 . As a function of the vortex core and Josephson junction–plane distance, the accompanying pinning potentials are quasi-degenerate in the near proximity to the Josephson junction plane, where the conventional-vortex-state pinning potential is the lower. Conditions facilitating the experimental observation of the new vortex state and a specific signature are briefly discussed.

Space-time nonlocal electrodynamic equations are derived for nonlinear vortex states of a Josephson junction in a film of thickness much smaller than the London penetration depth. The spectrum and damping of generalized Swihart waves propagating in such a junction are analyzed. The radiation damping constant associated with the possible emission of electromagnetic radiation is determined in the range of Swihart wave phase velocities exceeding the speed of light. The emission of radiation from nonlinear states having dimensions greater than the distance traversed by light in vacuum during the characteristic time of variation of the phase difference is investigated. It is shown that the flux density of radiation emitted by such states is localized in a plane orthogonal to the axis of the tunnel junction and depends weakly on the angle of observation in this plane.

The phenomenon of Cherenkov trapping of generalized Swihart waves by a moving vortex is established using an analytically solvable model. The quantization of the structure of the field of the trapped waves is manifested as quantization of the values of the velocity of the vortices.

We investigate theoretically how the proximity of an Abrikosov vortex influences the physical properties of a long Josephson junction. We find that dI c , the contribution to the critical current associated with the presence of the vortex, is generally positive ~the critical current is increased ! and is crucially dependent on the specific boundary conditions satisfied by the transport current. In the case in which the latter has a bulk component in the vicinity of the vortex, dI c is proportional to the coupling c between the vortex and the junction. The situation is however more complex when the transport current is purely a surface phenomenon. In this case dI c strongly depends on the distance between the vortex and the edges of the junction, and is in general much smaller than that of the bulk current case unless a special commensurability condition is met. In particular we show that a contribution to dI c proportional to c is obtained in this case only when an integer number of Josephson vortices can be accommodated between the location of the vortex and one of the edges of the junction. @S0163-1829~98!10137-6#

The approach of SteuerwaldLamb for obtaining exact solutions of the sineGordon equation is further developed through transformations by means of which complicated solutions of the corresponding ODEs are obtained without any explicit integration. Polynomial and nonpolynomial transformations are discussed and several of them are used to obtain breather and soliton solutions of the sineGordon equation. The obtained solutions are discussed from the point of view of the electrodynamics of the long Josephson junction.

Cherenkov radiation exists if a particle moves with the velocity equal to the phase velocity of the emitted waves. Electromagnetic waves in a long Josephson junction ~LJJ! are described by the sine-Gordon equation which has, in particular, soliton ~Josephson vortex! and linear wave ~Josephson plasma! solutions. A soliton behaves as a quasiparticle with its own characteristic mass and velocity. The highest

The dynamics of fluxons in coupled long Josephson junctions is considered. The condition for stochastic breaking of a bound state of fluxons under the action of ac-current is analytically derived and tested by numerical simulations.

A study is made of fluxon motion in a long Josephson junction with a local inhomogeneity (microresistor) in the presence of an alternating external current. Nonlinear resonances in the fluxon dynamics are considered. The process by which a fluxon trapped at an inhomogeneity is stochastically depinned under the influence of a periodic current is investigated analytically and numerically.

It is shown that a recursion operator can be used to examine the Lyapunov stability of non-integrable boundary-value problems. There is a detailed discussion of determining the asymptotic state in a long Josephson contact in an external magnetic field. This is reduced to examining the stability of the stationary solutions that satisfy certain boundary conditions and the sin-Gordon equation.

The RCSJ (Resistor-Capacitor Shunted Junction) model provides us an analytical formula for the conversion efficiency for a resonant Josephson effect mixer. An external rf signal is applied to a long Josephson junction operating in the fluxon oscillating regime. The sine-Gordon equation is used to investigate the dynamics of the phase-locking between the fluxon oscillations and the external signal. We obtain that it is possible to have conversion efficiency greater than unity.

We study a 1D array of Josephson coupled superconducting grains with kinetic inductance which dominates over the Josephson inductance. In this limit the dynamics of excess Cooper pairs in the array is described in terms of charge solitons, created by polarization of the grains. We analyze the dynamics of these topological excitations, which are dual to the fluxons in a long Josephson junction, using the continuum sine-Gordon model. We find that their classical relativistic motion leads to saturation branches in the I-V characteristic of a ring-shaped array. We then discuss the semiclassical quantization of the charge soliton, and show that it is consistent with the large kinetic inductance of the array. We study the dynamics of a quantum charge soliton in a ring-shaped array biased by an external flux through its center. If the dephasing length of the quantum charge soliton is larger than the circumference of the array, quantum phenomena like persistent current and coherent current oscillations are expected. As the characteristic width of the charge soliton is of the order of 100 \ensuremath{\mu}m, it is a macroscopic quantum object. We discuss the dephasing mechanisms which can suppress the quantum behavior of the charge soliton. \textcopyright{} 1996 The American Physical Society.

We propose a tunable macroscopic quantum system based on two fractional vortices. Our analysis shows that two coupled fractional vortices pinned at two artificially created κ discontinuities of the Josephson phase in a long Josephson junction can reach the quantum regime where coherent quantum oscillations arise. For this purpose we map the dynamics of this system to that of a single particle in a double-well potential. By tuning the κ discontinuities with injector currents, we are able to control the parameters of the effective double-well potential as well as to prepare a desired state of the fractional vortex molecule. The values of the parameters derived from this model suggest that an experimental realization of this tunable macroscopic quantum system is possible with today's technology., Video Abstract, publishedVersion

Chaotic responses induced by an applied rf signal on the long Josephson junction influenced by a constant dc-driven field are investigated by means of a model based on the sine-Gordon equation. We assume that the localized nonlinear excitations present in the system as initial data are the breatherlike mode. Thus, in order to analyze in detail the onset of the complicated irregular behavior (chaos), we employ collective coordinate theory to derive the total Hamiltonian and the dissipative function in terms of the breather width. The appearance of chaos in this system is predicted by the Melnikov theory and a few numerical treatments. A threshold for chaos as a function of the physical parameters of the system is found. Finally, the Poincar\'e sections, which allow us to see clearly the phenomenon in the nondissipative case, is compared to the analytical prediction and good agreement is obtained.

With a slight modification to the control line and its bias configuration, a long Josephson junction vortex flow transistor structure can become a so-called fluxonic diode containing fluxon and antifluxon "doped" regions in analogy to a pn junction. Such structures have been made with Nb-Pb tunnel junctions allowing testing of the same device with a number of different doping configurations. This paper compares experimental results with a one dimensional numerical simulation. Different configurations for the diode have been modeled with Stewart-McCumber loss parameters ranging between 50 and 1400. The simulation clarifies the origin of a number of experimental observations, including a peculiar dependence of resonance induced step behavior on loss parameter, and a limit to the value of the gradient of doping in the transition region below which an asymmetric I-V curve representing forward and reverse biases is obtained. In forward bias, the I-V curve above a threshold current is roughly linear and devoid of resonance structure, provided injection of carriers occurs from one region to the other. Injection is a function of loss and the asymmetry of doping. >

Soliton dynamics in a perturbed sine-Gordon equation modeling a long Josephson junction is investigated. Solitons are found to exist in both simple and chaotic forms. Soliton synchronization by an alternating magnetic field is analysed. Current-voltage characteristics of Josephson junction are plotted.

It is shown that vortex-anti-vortex pairs, thermally excited in a long and thin Josephson junction, lead to resistivity of the junction imitating the 2D Kosterlitz-Thouless transition. In this case there is no sharp transition point and the resistive state exists at all finite temperatures. Resistivity and voltage current characteristics are calculated in a range of temperatures.

The motion of fluxons in a long Josephson junction with point-like inhomogeneities (microresistors) and a dissipative loss is studied in a semi-analytical and fully numerical manner. It is found that the dynamic behaviour of fluxons is markedly changed by the combined effect of microresistors and an AC drive, i.e. the AC drive allows, via the microresistors, the fluxons to overcome a dissipative resistance and to move forward linearly. A physical interpretation of the significant novel phenomenon is given. First, the microresistors generate a new type of inherent localized structure, the so-called impurity mode. Then, the impurity modes are excited and amplified by the AC drive. Finally, the fluxon gains, through the strong fluxon-impurity mode (microresistor) interactions, kinetic energy to overcome the attractive potentials of the microresistors and the dissipative resistance, and it escapes from the microresistors eventually.

We have measured the bidirectional propagation of microwaves through a long Josephson junction in a flux-flow regime. We demonstrate that the transmitted microwave power depends on the direction of microwave propagation with respect to the direction of the flux flow. This nonreciprocal behavior is explained by the interaction of the microwave signal with the moving fluxon chain inside the junction. Thus a long junction may act as an on-chip isolator for external microwave signals, with its transmission properties being fully controlled by the bias current and in-plane magnetic field.

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\pi$ slips of the phase of the order parameter. However, in a finite-length wire coherent quantum phase-slips would manifest themselves simply as shifts of energy levels in the excitations spectrum of an electrical circuit incorporating this wire. The higher the phase-slips probability amplitude, the larger are the shifts. Phase-slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase-slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slips amplitudes random functions of time, and therefore turn energy levels shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a "slippery" wire. The slip-induced linewidths, despite being only of order 100 kHz, were resolved from the flux-dependent dephasing of the fluxonium qubit., Comment: 15 pages

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 $\lambda_J$ 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 $\lambda_J$) junction width is observed., Comment: 4 Figures, submitted to Phys. Lett. A

We investigate the phase dynamics of a long Josephson junction (LJJ) with two-gap superconductors. In this junction, two channels for tunneling between the adjacent superconductor (S) layers as well as one interband channel within each S layer are available for a Cooper pair. Due to the interplay between the conventional and interband Josephson effects, the LJJ can exhibit unusual phase dynamics. Accounting for excitation of a stable 2$\pi$-phase texture arising from the interband Josephson effect, we find that the critical current between the S layers may become both spatially and temporally modulated. The spatial critical current modulation behaves as either a potential well or barrier, depending on the symmetry of superconducting order parameter, and modifies the Josephson vortex trajectories. We find that these changes in phase dynamics result in emission of electromagnetic waves as the Josephson vortex passes through the region of the 2$\pi$-phase texture. We discuss the effects of this radiation emission on the current-voltage characteristics of the junction., Comment: 14 pages, 6 figures

Commensurability between a static fluxon chain and a periodic lattice of inhomogeneities in a long Josephson junction has been studied experimentally. Some of the equidistant peaks in the I c ( H )-curve are suppressed as predicted by the theory of Fehrenbacher et al. But, unexpectedly, a suppression of subharmonic peaks is also observed.

A change of the I-V characteristics of a long Josephson junction, operating in the zero-field single-fluxon regime, under the action of a ``hot spot'' (e.g., created by a focused electron beam) is calculated analytically by means of the perturbation theory, and also investigated numerically. The change of the average voltage at a given value of the bias current is calculated as a function of the hot spot-position. The overlap Josephson junction geometry is considered in detail, while the inline one is briefly discussed. A good accord between analytical and numerical results is found. The results are relevant for the interpretation of the low-temperature scanning electron microscopy experiments on imaging the fluxon dynamic states in a long Josephson junction.

Breathers excitations in a driven long Josephson junction influenced by a localized impurity due to a spatial variation of the inductance are discussed. By use of the perturbation method, it is shown that, in the absence of the bias current, the breather can break into a fluxon-antifluxon pair (ƒ ƒ ) , for values of the inductance greater than a threshold value (lothr). It is also seen that when the bias current is greater than a threshold value (ηthr, lo), the breather can convert into a ƒ ƒ for every value of the inductance. An approximate frequency for the breather is calculated in this framework.

Рассмотрено поведение длинного джозефсоновского перехода при протекании через него постоян- ного электрического тока. Установлено, что поведение распределения тока в длинном джозеф- соновском переходе аналогично поведению длинного упругого стержня-консоли при продольном изгибе. Кроме того, показано, что проникающие в одномерный переход вихри магнитного пото- ка есть аналог цепочки спинов во внешнем поле, ориентация которых зависит от соотношения собственного и внешнего магнитных полей, т.е. длинный джозефсоновский переход может рас- сматриваться как "динамическая доменная структура". The behaviour of long Josephson junction surveyed at course through it of a constant electric current. It is established, that behaviour of allocation of a current in long Josephson junction analog to behaviour long elastic rods-cantilevers at a buckling. Besides it is shown, that curls of a magnetic flux penetrating into the one-dimensional junction are analog of a line-up of spins in an external field which orientation depends on a relation of a natural and exterior magnetic field, i.e. long Josephson junction can be considered as dynamic domain structure.

The magnetization curves, M J ( H ), of long Josephson junction are computed from the dc Josephson equation with gauge-invariant phase. They are found to be reversible if α≡ L λ J , where L and λ j are the junction length and the Josephson penetration depth, respectively. Irreversibility starts from α=4, and when α⪢4, the M J ( H ) curve is similar to that of type-II superconductors with a surface barrier. The corresponding fields for first vortex entry and last vortex exit are H 1 J =2 J maxλ J , where J max is the maximum local written current density, and H 2 J , which has a small positive value.

The equilibrium velocity of a 2π-kink in a long Josephson junction is calculated analytically for low bias currents using the expression for the tunnel current from microscopic theory. The result is compared to the results of numerical simulations and excellent agreement is found, but the dynamics is very sensitive to the detailed form of the complex current amplitudes.

All-refractory material superconducting millimeter-wave oscillators have been designed and investigated experimentally with different superconductor-insulator-superconductor (SIS) mixers integrated on the same chip. Tested structures include a flux-flow oscillator (FFO) based on a long Josephson junction, a coupling section, and an SIS detector with tuned out junction capacitance. Coupling sections were designed as multistep microstrip quarter-wave impedance transformers. All junctions have been fabricated on the basis of a high-quality trilayer Nb-AlO/sub x/-Nb process. Microwave oscillations in the frequency range 75-500 GHz have been detected experimentally. The level of delivered power was estimated from the pumped I-V curve of the strongly coupled single junction detector. Coupled power levels higher than 0.1 mu W at 256 GHz were achieved. A spectral linewidth of the FFO of less than 1 MHz has been estimated experimentally. The first attempt to create an integrated receiver based on an FFO and an SIS array mixer integrated on the same chip was made in the 2-mm wavelength band. >

The authors report on the coupling of millimeter and submillimeter waves from a long (3- mu m*350- mu m) Josephson junction to a small (2- mu m*2- mu m) superconductor-insulator-superconductor (SIS) junction by using a center-fed interdigital capacitor. Coupled power at around 100 GHz and 261 GHz was observed. Experiments confirm that the critical current density j/sub c/ of a long junction determines the fluxon motion. Coupled irradiation (>3nW) at around 100 GHz, which corresponds to resonant soliton oscillations in low j/sub c/ samples (250 A/cm/sup 2/ to 1000 A/cm/sup 2/), is detected by the SIS junction. The incident power to the SIS detector junction could be tuned with only little frequency pulling by adjusting the current bias of the oscillator. For j/sub c/>1000 A/cm/sup 2/, coupled radiation at around 100 GHz (about 3 nW) and 261 GHz (4.6 nW), from flux-flow oscillations, is also clearly seen. Flux-flow radiation at 350 GHz is also observed. It is concluded that a large j/sub c/ value is preferable for high-frequency flux-flow oscillators. >

Interaction of a fluxon with an rf radiation emitted into a long Josephson junction is investigated analytically and numerically. We use a model based on the sine-Gordon equation driven by a periodic force at the boundary with the frequency larger than the plasma frquency of the junction. It is shown that due to excitation of a standing linear wave by the driving force, the fluxon motion is strongly influenced by a periodic (averaged) potential similar to the Peierls-Nabarro potential in a discrete chain. This effective potential decreases in the direction of the boundary where the external rf drive is applied, so that the fluxon always moves to the active boundary. We calculate the fluxon parameters and confirm our analytical predictions by direct numerical simulations.

The dynamics of discrete-one-dimensional parallel arrays of Josephson junctions has been studied experimentally and numerically. The energy barriers for vortex motion from cell to cell have been calculated as a function of the discreteness parameter, the ratio of the Josephson inductance to the self-inductance of the cell. The experimental data show resonances in the current-voltage characteristic, analogous to Fiske steps in a single long Josephson junction. These steps provide a novel experimental method for measuring the self-inductance of 1D parallel arrays. >

A long Josephson junction containing regions with a phase shift of pi is considered. By exploiting the defect modes due to the discontinuities present in the system, it is shown that Josephson junctions with phase-shift can be an ideal setting for studying localized mode interactions. A phase-shift configuration acting as a double-well potential is considered and shown to admit mode tunnelings between the wells. When the phase-shift configuration is periodic, it is shown that localized excitations forming bright and dark solitons can be created. Multi-mode approximations are derived confirming the numerical results., Comment: 4 pages, to appear in Phys. Rev. B

We study numerically a mechanism of vortex formation in a long Josephson junction within the framework of the one-dimensional sine-Gordon model. This mechanism is switched on below the critical temperature. It is shown that the number of fluxons versus velocity of cooling roughly scales according to the power law with the exponent of either 0.25 or 0.5 depending on the temperature variation in the critical current density.