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1.
Two-Dimensional Discrete Gap Breathers in a Two-Dimensional Diatomic β Fermi--Pasta--Ulam Lattice 下载免费PDF全文
We study the existence of two-dimensional discrete breathers in a two-dimensional face-centred square lattice consisting of alternating light and heavy atoms, with nearest-neighbour coupling containing quartic soft or hardnonlinearity. This study is focused on two-dimensional breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of existence of two-dimensional gap breathers by using the numerical method, the local anharmonicity approximation and the rotating wave approximation. We obtain six types of two-dimensional gap breathers, i.e., symmetric, mirror-symmetric and asymmetric, no matter whether the centre of the breather is on a light or a heavy atom. 相似文献
2.
In this paper we study the existence and stability of two-dimensional discrete gap
breathers in a two-dimensional diatomic face-centered square lattice
consisting of alternating light and heavy atoms, with on-site
potential and coupling potential. This study is focused on
two-dimensional breathers with their frequency in the gap that
separates the acoustic and optical bands of the phonon spectrum. We
demonstrate the possibility of the existence of two-dimensional gap
breathers by using a numerical method. Six types of two-dimensional
gap breathers are obtained, i.e., symmetric, mirror-symmetric and
asymmetric, whether the center of the breather is on a light or a
heavy atom. The difference between one-dimensional discrete gap
breathers and two-dimensional discrete gap breathers is also
discussed. We use Aubry's theory to analyze the stability of
discrete gap breathers in the two-dimensional diatomic face-centered
square lattice. 相似文献
3.
Periodic, Quasiperiodic and Chaotic Discrete Breathers in a Parametrical Driven Two-Dimensional Discrete Klein-Gordon Lattice 下载免费PDF全文
We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver. 相似文献
4.
Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein--Gordon lattice 下载免费PDF全文
We study a two-dimensional (2D) diatomic lattice of anharmonic
oscillators with only quartic nearest-neighbor interactions, in
which discrete breathers (DBs) can be explicitly constructed by an
exact separation of their time and space dependence. DBs can stably
exist in the 2D discrete diatomic Klein--Gordon lattice with hard
and soft on-site potentials. When a parametric driving term is
introduced in the factor multiplying the harmonic part of the
on-site potential of the system, we can obtain the stable
quasiperiodic discrete breathers (QDBs) and chaotic discrete
breathers (CDBs) by changing the amplitude of the driver. But the
DBs and QDBs with symmetric and anti-symmetric profiles that are
centered at a heavy atom are more stable than at a light atom,
because the frequencies of the DBs and QDBs centered at a heavy atom
are lower than those centered at a light atom. 相似文献
5.
The system consisting of a chain of parametrically driven and damped nonlinear coupled pendula with a mass impurity is studied by means of a discrete version of the envelope function approach. An analogue of the parametrically driven damped nonlinear Schodinger equation with an impurity term is derived from the original lattice equation. Analytical solutions of impurity pinned high-frequency breathers and kinks are obtained. The results show that the mass impurity has striking influence on the high-frequency modes. In addition, we perform numerical simulations, showing that the light mass impurity has a stabilizing effect on the chain. The breathers seeding chaos in the homogeneous chain are pinned on a suitable light impurity to pull the chain from the chaotic state. 相似文献
6.
The density of phonon states at various temperatures has been calculated for crystals with the NaCl structure with equal and strongly differing weights of anions and cations. It has been shown that, in the crystal with a considerable difference in the weights of components, a wide band gap exists in the spectrum of phonon states, which leads to spontaneous excitation of nonlinear localized vibrational modes??gap discrete breathers having frequencies inside the band gap, if the temperature is sufficiently high. It has been found that the peak of the density of phonon states lying above the spectrum of linear vibrations appears at elevated temperatures, which can indicate the existence of discrete breathers with corresponding frequencies. It has been noted that, previously, the existence of gap discrete breathers in the NaI crystal at 555 K was shown experimentally. The presented results bring up the question of the theoretical justification and experimental observation of the breathers with frequencies above the phonon spectrum. 相似文献
7.
K.Ø. Rasmussen S. Aubry A.R. Bishop G.P. Tsironis 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(1):169-175
We study the dynamics of the discrete nonlinear Schr?dinger lattice initialized such that a very long transitory period of
time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the
energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived,
their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases
we report the surprising observation that the energy content in the discrete breather population increases. We interpret these
observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather
cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency
discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather
tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing
discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.
Received 21 January 1999 and Received in final form 20 September 1999 相似文献
8.
Compact-like discrete breather and its stability in a discrete monatomic Klein--Gordon chain 下载免费PDF全文
This paper studies a discrete one-dimensional monatomic
Klein--Gordon chain with only quartic nearest-neighbor interactions,
in which the compact-like discrete breathers can be explicitly
constructed by an exact separation of their time and space
dependence. Introducing the trying method, it proves that
compact-like discrete breathers exist in this nonlinear system. It
also discusses the linear stability of the compact-like discrete
breathers, when the coefficient (β) of quartic on-site
potential and the coupling constant (K4) of quartic interactive
potential satisfy the given conditions, they are linearly stable. 相似文献
9.
We introduce an extended nonlinear Schrödinger (ENLS) equation describing the dynamics of modulated waves in a nonlinear discrete electrical transmission line (NLTL) with nonlinear dispersion. We show that this equation admits envelope dark solitary wave with compact support, with width and speed independent of the amplitude, as a solution. Analytical criteria of existence and stability of this solution are derived. In particular, we show that the modulated compact wave may exist in the NLTL depending on the frequency range of the chosen carrier wave, for physically realistic parameters. The stability of compact dark solitary wave is confirmed by numerical simulations of this ENLS equation and the exact equations of the network. 相似文献
10.
《Physics Reports》1998,295(5):181-264
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurrence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices — quantum breathers.Finally we will formulate a new conceptual approach capable of predicting whether discrete breathers exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response. 相似文献
11.
It has been shown recently that a moving discrete breathers localized in one close-packed atomic row can be excited in a two-dimensional monoatomic crystal with Morse interaction. In this work, a motionless discrete breathers having the threefold symmetry axis has been excited in the same crystal. The initial conditions for the excitation of such discrete breathers are set by the superposition of a bell-shaped function on a planar nonlinear phonon mode with the wave vector lying at the edge of the Brillouin zone. In addition, the displacement of the centers of atomic oscillations from the center of the discrete breathers owing to the asymmetry of the Morse potential is taken into account. The results obtained make it possible to approach the search for highly symmetric discrete breathers in three-dimensional crystals. 相似文献
12.
Light propagation in one-dimensional nonlinear waveguide arrays with self-defocusing intensity-resonant nonlinearity is investigated
theoretically. We study thoroughly conditions for existence and stability of both gap and discrete dark solitons. According
to the linear stability analysis both fundamental types (on-site and intersite) of gap solitons may be stable. Discrete dark
solitons are unstable except in the low-power regime and, depending on system parameters, evolve into either gray solitons,
breathers, or background radiation. Mobility of these solitons is analyzed by the free energy concept: gap solitons are immobile
but dark solitons can be easily set in motion. 相似文献
13.
We investigate the properties of modulational instability and discrete breathers in the cubic-quintic discrete nonlinear Schrödinger equation. We analyze the regions of modulational instabilities of nonlinear plane waves. Using the Page approach [J.B. Page, Phys. Rev. B 41 (1990) 7835], we derive the conditions for the existence and stability for bright discrete breather solutions. It is shown that the quintic nonlinearity brings qualitatively new conditions for stability of strongly localized modes. The application to the existence of localized modes in the Bose-Einstein condensate (BEC) with three-body interactions in an optical lattice is discussed. The numerical simulations agree with the analytical predictions. 相似文献
14.
Crystals having a gap in the phonon spectrum can maintain gap discrete breathers (DBs), i.e., nonlinear localized oscillatory
modes existing in the absence of defects and having a frequency lying in the gap. The lifetime of gap DBs in a two-dimensional
perfect crystal of the composition A
3
B in thermal equilibrium has been studied by the molecular dynamics method. As was shown earlier, the existence of gap DBs
in such a crystal is provided by the presence of a wide gap in the phonon spectrum if the component mass ratio m
A
/m
B
is sufficiently large. For comparison, a crystal with a relatively small ratio m
A
/m
B
is considered when the gap in the spectrum is absent and the existence of gap DBs is impossible in the case of a weak nonlinearity
realized in the considered case. It has been shown that, in contrast to the opposite case, in a crystal maintaining gap DBs,
long-lived localized oscillatory modes of large amplitude can emerge, whose concentration and lifetime increase with temperature. 相似文献
15.
We study a one-dimensional Sine-Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions,
in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can
stably exist in the one-dimensional Sine-Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When
a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system,
we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the
driver. 相似文献
16.
We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a time-periodic localized scattering potential for plane waves. We consider the case of elastic one-channel scattering, when the frequencies of incoming and transmitted waves coincide, but the breather provides with additional spatially localized ac channels whose presence may lead to various interference patterns. The dependence of the transmission coefficient on the wave number q and the breather frequency Omega(b) is studied for different types of breathers: acoustic and optical breathers, and rotobreathers. We identify several typical scattering setups where the internal time dependence of the breather is of crucial importance for the observed transmission properties. 相似文献
17.
The mobility of high-frequency discrete breathers in monatomic chains with nonlinear interatomic potentials of the nearest neighbors is considered. It was found that the odd (cubic and fifth) anharmonicity strongly affects the mobility of breathers, sharply increasing the distance that it propagates without being trapped. It was also found that the correctly chosen fifth anharmonicity leads to an inversion of stability between the bond-centered and site-centered breathers and to the low-radiative propagation of discrete breathers along the chain. 相似文献
18.
The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi–Pasta–Ulam (FPU) and
related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems.
Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the
quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced
by the harmonic term stabilize the discrete breather by suppressing the breather’s tendency to delocalize and disperse. We
conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these
systems. 相似文献
19.
The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. 相似文献
20.
S. V. Dmitriev L. Z. Khadeeva A. I. Pshenichnyuk N. N. Medvedev 《Physics of the Solid State》2010,52(7):1499-1505
The properties of gap discrete breathers in three-dimensional and two-dimensional crystals of the composition A
3
B with interatomic bonds described by the Morse potential have been investigated by the molecular dynamics method for different
ratios between the masses of components m
A
/m
B
. The transition to a thermal equilibrium from a state far from equilibrium has been studied for the two-dimensional crystal.
In this case, a short-wavelength phonon vibrational mode is excited in the crystal. This mode appears to be modulationally
unstable for not too small amplitudes. During the transition to the state characterized by a uniform energy distribution between
all vibrational modes of the crystal, the energy is localized in the form of gap discrete breathers, which exist in time intervals
that exceed their oscillation period by several orders of magnitude. 相似文献