相关论文: Energy thresholds for discrete breathers

We consider the discrete p-Schr\"odinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order alpha = p-1 >1. Using a mapping approach, we…

The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations. Following an earlier work [Comm. Math. Phys. {\bf 302},…

We discuss the existence of breather solutions for a Discrete Nonlinear Schr\"odinger equation in an infinite $N$-dimensional lattice, involving site dependent anharmonic parameter. We give a simple proof on the existence of (nontrivial)…

It is well known that any amount of energy injected in a harmonic oscillator which is resonant and weakly coupled with a second harmonic oscillator, tunnels back and forth between these two oscillators. When the two oscillators are…

We describe, for the first time, the full 2D scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an…

Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and…

We present a simple numerical method for the discrete breather construction based on the idea of the pair synchronization of the particles involved in the breather vibration. It can be used for obtaining exact breather solutions in…

We investigate the energy relaxation process produced by thermal baths at zero temperature acting on the boundary atoms of chains of classical anharmonic oscillators. Time-dependent perturbation theory allows us to obtain an explicit…

Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging,…

We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical…

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci.…

A nonlinear chain with six-order polynomial on-site potential is used to analyze the evolution of the total to kinetic energy ratio during development of modulational instability of extended nonlinear vibrational modes. For the on-site…

We show for the first time that highly localized in-plane breathers can propagate in specific directions with minimal lateral spreading in a model 2-D hexagonal non-linear lattice. The lattice is subject to an on-site potential in addition…

The calculation of the discrete atomistic energy of a crystal near the continuum limit encounters difficulties caused by the geometric discrepancy between the continuum region occupied by the body, and the discrete collection of lattice…

For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions:…

One-dimensional chain of pointwise particles harmonically coupled with nearest neighbors and placed in six-order polynomial on-site potentials is considered. Power of the energy source in the form of single ac driven particles is calculated…

We prove the existence of time-periodic solutions and spatially localised solutions (breathers), in general nonlinear Klein-Gordon infinite lattices. The existence problem is converted into a fixed point problem for an operator on some…

In this paper we investigate the emergence of time-periodic and and time-quasiperiodic (sometimes infinitely long lived and sometimes very long lived or metastable) solutions of discrete nonlinear wave equations: discrete sine Gordon,…

We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schr\"{o}dinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak…

In strained monoatomic chains with Lennard-Jones interactions, we revealed a stable static non-homogeneous structure appearing as a result of a certain phase transition. Positions of individual particles in this structure form an exact…