288 research outputs found
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
A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation
In this paper we develop a finite-difference scheme to approximate radially
symmetric solutions of the initial-value problem with smooth initial conditions
in an open sphere around the origin, where the internal and external damping
coefficients are constant, and the nonlinear term follows a power law. We prove
that our scheme is consistent of second order when the nonlinearity is
identically equal to zero, and provide a necessary condition for it to be
stable order n. Part of our study will be devoted to compare the physical
effects of the damping coefficients
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
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 -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 -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
-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
Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices
In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the
tangent bifurcation of the band edge modes () of nonlinear Hamiltonian
lattices made of coupled oscillators. Introducing the concept of {\em
partial isochronism} which characterises the way the frequency of a mode,
, depends on its energy, , we generalize these results and
show how the bifurcation energies of these modes are intimately connected to
their degree of isochronism. In particular we prove that in a lattice of
coupled purely isochronous oscillators ( strictly constant),
the in-phase mode () never undergoes a tangent bifurcation whereas the
out-of-phase mode () does, provided the strength of the nonlinearity in
the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger
equation governing the slow modulations of small-amplitude band edge modes and
show that its nonlinear exponent is proportional to the degree of isochronism
of the corresponding orbits. This equation may be seen as a link between the
tangent bifurcation of band edge modes and the possible emergence of localized
modes such as discrete breathers.Comment: 23 pages, 1 figur
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 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
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
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
Solitary Wave Interactions In Dispersive Equations Using Manton's Approach
We generalize the approach first proposed by Manton [Nuc. Phys. B {\bf 150},
397 (1979)] to compute solitary wave interactions in translationally invariant,
dispersive equations that support such localized solutions. The approach is
illustrated using as examples solitons in the Korteweg-de Vries equation,
standing waves in the nonlinear Schr{\"o}dinger equation and kinks as well as
breathers of the sine-Gordon equation.Comment: 5 pages, 4 figures, slightly modified version to appear in Phys. Rev.
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