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1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
On some classes of two-dimensional local models in discrete two-dimensional monatomic FPU lattice with cubic and quartic potential 下载免费PDF全文
This paper discusses the two-dimensional discrete monatomic
Fermi--Pasta--Ulam lattice, by using the method of multiple-scale and
the quasi-discreteness approach. By taking into account the
interaction between the atoms in the lattice and their nearest
neighbours, it obtains some classes of two-dimensional local models
as follows: two-dimensional bright and dark discrete soliton
trains, two-dimensional bright and dark line discrete breathers, and
two-dimensional bright and dark discrete breather. 相似文献
8.
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
9.
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
10.
Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method 下载免费PDF全文
D. B. Dhaigude & Gunvant A. Birajdar 《advances in applied mathematics and mechanics.》2014,6(1):107-119
In this paper we find the solution of linear as well as nonlinear
fractional partial differential equations using discrete Adomian
decomposition method. Here we develop the discrete Adomian decomposition
method to find the solution of fractional discrete diffusion equation,
nonlinear fractional discrete Schrodinger equation, fractional discrete
Ablowitz-Ladik equation and nonlinear fractional discrete Burger's equation.
The obtained solution is verified by comparison with exact solution when $\alpha=1$. 相似文献
11.
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
12.
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
13.
Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations 下载免费PDF全文
In this paper, the improved Jacobian elliptic function expansion
approach is extended and applied to constructing discrete solutions
of the semi-discrete coupled modified Korteweg de Vries (mKdV)
equations with the aid of the symbolic computation system Maple.
Some new discrete Jacobian doubly periodic solutions are obtained.
When the modulus $m \rightarrow 1$, these doubly periodic solutions
degenerate into the corresponding solitary wave solutions, including
kink-type, bell-type and other types of excitations. 相似文献
14.
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
15.
Exact solution and exotic coherent solition structures of the (2+1)—dimensional generalized nonlinear Schroedinger equation 下载免费PDF全文
In this paper,a variable separation approach is used to obtain localized coherent structures of the (2 1)-dimensional generalized nonlinear Schroedinger equation:Iφt-(α-β)φxx (α β)φyy-2λφ[(α β)(∫-∞^x|φ|y^2ydx u1(y,t))-(α-β)(∫-∞^y|φ|x^2dy u2(x,t))]=0,By applying a special Baecklund transformation and introducing arbitrary functions of the seed solutions,the abundance of the localized structures of this model are derived.By selecting the arbitrary function appropriately,some special types of localized excitations such as dromions,dromion lattice,breathers and istantons are constructed. 相似文献
16.
We investigate the wavefronts depinning in current biased, infinitely long semiconductor superlattice systems by the method of discrete mapping and show that the wavefront depinning corresponds to the discrete mapping failure. For parameter values near the lower critical current in both discrete drift model (DD model) and discrete drift-diffusion model (DDD model), the mapping failure is determined by the important mapping step from the bottom of branch to branch α. For the upper critical parameters in DDD model, the key mapping step is from branch γ to the top of the corresponding branch α and we may need several active wells to describe the wavefronts. 相似文献
17.
《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
18.
19.
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
20.
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