Breathers In Lattices Research Articles

Breathers in lattices with alternating strain-hardening and strain-softening interactions.

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving, are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a nonlinear Schrödinger equationto construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.

On Bright and Dark Breathers in Lattices with Saturable Nonlinearity

In the past two decades the special attention is devoted to the strongly localized modes [1] which are promising candidates for guiding, steering, and switching of light beams in the nonlinear optical lattices. The effect of energy localization through discreteness and nonlinearity is universal and relevant for many non-optical systems, such as DNA-promoter dynamics [2], discrete breathers in a Josephson ladder [3], localized modes in the anharmonic crystals [4], or localization of matter waves in the Bose–Einstein condensates using optically-induced periodic potentials [5]. Bright discrete solitons have been studied in detail in photonic lattices exhibiting cubic, quadratic, saturable, and nonlocal nonlinearity [1, 6–9]. Because of various experimental difficulties and demand for higher input power dark solitons are investigated discernible rarely when compared to their bright analog [10, 11]. Very recently, stable propagation of on-site and inter-site dark solitons were experimentally observed in the self-defocusing lithium niobate waveguide arrays with saturable nonlinearity at microwatt power level [12, 13]. In this paper the comparative study of the moving localized bright and dark modes in lattices with saturable nonlinearity [14] is presented. This study is based on the grand canonical free energy concept [15] and analysis of the eigenvalue spectra of the localized configurations.

Dynamics of dark breathers in lattices with saturable nonlinearity

The problems of the existence, stability, and transversal motion of the discrete dark localized modes in the lattices with saturable nonlinearity are investigated analytically and numerically. The stability analysis shows existence of regions of the parametric space with eigenvalue spectrum branches with non-zeroth real part, which indicates possibility for the propagation of stable on-site and inter-site dark localized modes. The analysis based on the conserved system quantities reveals the existence of regions with a vanishing Peierls-Nabarro barrier which allows transverse motion of the dark breathers. Propagation of the stable on-site and inter-site dark breathers and their free transversal motion are observed numerically.

A regularized model equation for discrete breathers in anharmonic lattices with symmetric nearest-neighbor potentials

We propose a regularized continuum model equation for describing discrete breathers or intrinsic localized modes in one-dimensional anharmonic lattices with symmetric nearest-neighbor potentials. Exact stationary breather solutions with purely hard quartic anharmonicity, as well as approximate stationary breather solutions in the general case, are found. The application of the multiple scales analysis indicates the movability of the small-amplitude breather solutions. The results of numerical simulations for the model equation fully support the analytical solutions. As regards the breather–breather collisions, the continuum model shares many common features with its discrete counterpart, which provides an opportunity to clarify the energy exchange mechanism for collisions between discrete breathers in lattices.

Existence and stability of breathers in lattices of weakly coupled two-dimensional near-integrable Hamiltonian oscillators

A method of proving the existence of breathers in lattices of two-dimensional weakly coupled Hamiltonian oscillators is presented. This method has the advantage that provides a first approximation of the initial conditions of the breather solution together with its linear stability. Since the proof relies on the use of action-angle variables, we also present a method to perform the calculations without knowledge of the specific transformation. We illustrate the results in a lattice of quartic oscillators and in another one that consists of coupled 2D Morse oscillators. Finally, we examine the possibility of extending these results in lattices of more than two degrees of freedom per lattice site.

Numerical approximation of breathers in lattices with nearest-neighbor interactions.

A numerical method is presented for accurately approximating time-periodic and spatially localized solutions known as (discrete) breathers, of the equations of motion describing lattices with one degree-of-freedom per lattice site and nearest-neighbor interactions. Our method is an extension of an approximation suggested by Tsironis [J. Phys. A 35, 951 (2002)], gives more accurate results than the rotating wave approximation and is more universally applicable for these lattices. As an illustration, the method is applied here to several one- and two-dimensional lattices.

Discrete Breathers in Lattices of Coupled Oscillators**The project supported by National Natural Science Foundation of China (19805002), Special Funds for Major State Basic ResearchProjects of China, Foundation for University Key Teachers by the Ministry of Education of China, Hong Kong RGC Foundation and Hong Kong Baptist University FRG Foundation of China

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.

Dependence of thermal conductivity on discrete breathers in lattices.

We study the properties of heat conduction in chains of coupled particles subjected to different anharmonic on-site potentials. Particular emphasis is placed on the role of breathers in saturation of the thermal conductivity for chains with hard anharmonicity. When the chain particles are subject to on-site potentials with soft anharmonicity, we find a characteristic temperature, below which the conductivity decreases but while above which it increases.