Driven Intrinsic Localized Modes in a Coupled Pendulum Array

Intrinsic localized modes (ILMs), also called discrete breathers, are directly generated via modulational instability in an array of coupled pendulums. These ILMs can be stabilized over a range of driver frequencies and amplitudes. They are characterized by a pi-phase difference between their center and wings. At higher driver frequencies, these ILMs are observed to disintegrate via a pulsating instability, and the mechanism of this breather instability is investigated.Comment: 5 pages, 6 figure

Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond

A novel, protean, topological soliton has recently been shown to emerge in systems of repulsive particles in cylindrical geometries, whose statics is described by the number-theoretical objects of phyllotaxis. Here we present a minimal and local continuum model that can explain many of the features of the phyllotactic soliton, such as locked speed, screw shift, energy transport and, for Wigner crystal on a nanotube, charge transport. The treatment is general and should apply to other spiraling systems. Unlike e.g. Sine-Gornon-like systems, our solitons can exist between non-degenerate structure, imply a power flow through the system, dynamics of the domains it separates; we also predict pulses, both static and dynamic. Applications include charge transport in Wigner Crystals on nanotubes or A- to B-DNA transitions.Comment: 8 Pages, 6 Figures, Phys Rev E in pres

Energy transmission in the forbidden bandgap of a nonlinear chain

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process ocurs at a threshold amplitude by sudden large energy flow, that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and sustained by an extremely simple theory.Comment: LaTex file, 6 figures, published in Phys Rev Lett 89 (2002) 13410

Scaling, self-similar solutions and shock waves for V-shaped field potentials

We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(\phi)| = |\phi|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with infinite number of degrees of freedom. The model has an interesting scaling symmetry of the 'on shell' type. We find self-similar as well as shock wave solutions of the field equation in that model.Comment: Two comments and one reference adde

Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions

Self-organized escape of oscillator chains in nonlinear potentials

We present the noise free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values

Tristability in the pendula chain

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.Comment: To appear in PR

Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide

We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{\"o}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasi-discrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments

Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system

Formation of Random Dark Envelope Solitons from Incoherent Waves

This letter reports experimental results on a new type of soliton: the random temporal dark soliton. One excites an incoherent large-amplitude propagating spin-wave packet in a ferromagnetic film strip with a repulsive, instantaneous nonlinearity. One then observes the random formation of dark solitons from this wave packet. The solitons appear randomly in time and in position relative to the entire wave packet. They can be gray or black. For wide and/or very strong spin-wave packets, one also observes multiple dark solitons. In spite of the randomness of the initial wave packets and the random formation processes, the solitons show signatures that are found for conventional coherent dark solitons.Comment: 10 pages, 4 figures, double-spaced preprint forma