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1.
Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice
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We study the existence and stability of two-dimensional discrete breathers in a two-dimensionai discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling. Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive) and the center of the two-dimensional gap breathers (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.
Compact-like discrete breather and its stability in a discrete monatomic Klein--Gordon chain
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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
4.
Bin-bin Lü 《Frontiers of Physics》2010,5(2):199
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
5.
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
6.
We study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers (DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e. these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi–Pasta–Ulam–Tsingou-β (FPUT-β) types, we find two crossovers of relaxation in general, i.e. a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-β type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices. 相似文献
7.
Periodic, Quasiperiodic and Chaotic Discrete Breathers in a Parametrical Driven Two-Dimensional Discrete Klein-Gordon Lattice
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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
8.
Existences and stabilities of bright and dark breathers in a general one-dimensional discrete monatomic Chain
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A general one-dimensional discrete monatomic model is investigated
by using the multiple-method. It is proven that the discrete bright
breathers (DBBs) and discrete dark breathers (DDBs) exist in this
model at the anti-continuous limit, and then the concrete models of
the DBBs and DDBs are also presented by the multiple-scale approach
(MSA) and the quasi-discreteness approach (QDA). When the results
are applied to some particular models, the same conclusions as those
presented in corresponding references are achieved. In addition, we
use the method of the linearization analysis to investigate this
system without the high order terms of $\varepsilon$. It is found
that the DBBs and DDBs are linearly stable only when coupling
parameter $\chi$ is small, of which the limited value is obtained by
using an analytical method. 相似文献
9.
XU Quan TIAN Qiang 《理论物理通讯》2009,51(1):153-156
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice. 相似文献
10.
《Physics letters. A》2020,384(4):126100
In this paper, we consider the interaction of small amplitude waves (phonons) with standing discrete breather (DB) in the one-dimensional chain of harmonically coupled particles interacting with the anharmonic one-site potential, which can be of hard-type or soft-type anharmonicity. The coefficients of phonon reflection and transmission are calculated numerically. It is found that for the case of hard-type anharmonicity (soft-type anharmonicity) DBs are more transparent for short-wavelength (long-wavelength) phonon waves, while they efficiently reflect long-wavelength (short-wavelength) phonons. In thermal equilibrium, when all phonons have equal energy density, it is found that for the same width of the transparency window, DB transmits less energy in the case of the hard-type anharmonicity. This is so because, in this case, DB reflects long-wavelength phonons, which have larger group velocity and hence greater contribution to the net energy flux through the DB. In this sense, DBs more efficiently suppress thermal conductivity in the chain with hard-type anharmonicity. Our results contribute to a better understanding of the role of discrete breathers in the heat flow in nonlinear chains. 相似文献
11.
Under harmonic approximation, this paper discusses the
linear dispersion relation of the one-dimensional chain. The existence
and evolution of discrete breathers in a general one-dimensional
chain are analysed for two particular examples of soft (Morse) and
hard (quartic) on-site potentials. The existence of discrete
breathers in one-dimensional and two-dimensional Morse lattices is
proved by using rotating wave approximation, local anharmonic
approximation and a numerical method. The localization and amplitude
of discrete breathers in the two-dimensional Morse lattice with on-site
harmonic potentials correlate closely to the Morse parameter a and
the on-site parameter к. 相似文献
12.
Two-dimensional discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials are investigated. Under the harmonic approximation, the linear dispersion relations for the triangular and the square lattices are discussed. The existence of discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials is proved by using local inharmonic approximation and the numerical method. The localization and amplitude of two-dimensional discrete breathers correlate closely to the Morse parameter a and the on-site parameter κ. 相似文献
13.
The dynamics of different kinds of discrete breathers in three types of one-dimensional monatomic chains with on-site and inter-site potentials are investigated. The existence and evolution of symmetric breather, antisymmetric breather, and multibreather in one-dimensional models are proved by using rotating wave approximation, local anharmonic approximation, and the numerical method. The linear stability of these breathers is investigated by using Lyapunov stable analysis. The localization and stability of breathers in three types of models correlate closely to the system nonlinear parameter β. 相似文献
14.
The discrete gap breathers (DGBs) in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω(ζ). With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller. 相似文献
15.
We consider a relation between discrete breathers (DBs) and nonlinear normal modes in some nonlinear monoatomic chains. The dependence of the breathers’ stability on the strength of interparticle interaction in the K4 chain (the chain with uniform on-site and intersite potentials of the fourth order) is investigated. A general method for constructing DBs which provides the pair synchronization between the individual particles’ vibrations is discussed. Many-frequency breathers as DBs of a new type and quasibreathers [introduced in Physical Review E 74 (2006) 036608] are analyzed. 相似文献
16.
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are stable, and their broad intersite counterparts are marginally stable, featuring a virtually vanishing real instability eigenvalue. The solitons become unstable in the case of the slowly relaxing nonlinearity. The character of the instability alters with the increase of the delay time, which leads to a change in the dynamics of unstable discrete solitons. They form robust localized breathers in rapidly relaxing media, and decay into oscillatory diffractive pattern in the lattices with a slow nonlinear response. Marginally stable solitons can freely move across the lattice. 相似文献
17.
Manuel G. Velarde Alexander P. Chetverikov Werner Ebeling Sergey V. Dmitriev Victor D. Lakhno 《The European Physical Journal B - Condensed Matter and Complex Systems》2016,89(10):233
The excitation of solitons and discrete breathers (pinned or otherwise, also known asintrinsic localized modes, DB/ILM) in a one-dimensional lattice, also denoted as a chain,is considered when both on-site and inter-site vibrations, coupled together, are governedby the empirical Morse interaction. We focus attention on the transformation of the formerinto the latter as the relative strength of the on-site potential to that of theinter-site potential is increased. 相似文献
18.
Two-Dimensional Discrete Gap Breathers in a Two-Dimensional Diatomic β Fermi--Pasta--Ulam Lattice
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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
19.
Kevrekidis PG Rasmussen KO Bishop AR 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(2):2006-2009
We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schrodinger equation on a square lattice reveals three different types of breathers. Considering an elementary plaquette, the most unstable mode is centered on the plaquette, the most stable mode is centered on its vertices, while the intermediate (but also unstable) mode is centered at the middle of one of the edges. Below the turning points of each branch in a frequency-power phase diagram, the construction methodology fails and a continuation method is used to obtain the unstable branches of the solutions until a triple point is reached. At this triple point, the branches meet and subsequently bifurcate into the final state of an extended phonon mode. 相似文献
20.
ZHENG Zhi-Gang 《理论物理通讯》2001,35(2):137-142
Discrete breathers are generic solutions for the dynamics of nonlinearly coupled oscillators. We show that discrete breathers can be observed in low-dimensional and high-dimensional lattices by exploring the sinusoidally coupled pendulum. Loss of stability of the breather solution is studied. We also find the existence of discrete breather in lattices with parameter mismatches. Breather phase synchronization is exhibited for the coupled chaotic oscillators. 相似文献