Related papers: Some breathers and multi-breathers for FPU-type ch…
We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…
The evolution towards equipartition in the $\beta$-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally…
The Fermi-Pasta-Ulam (FPU) problem consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is…
It is demonstrated that the breather solutions recently discovered in the weakly coupled topological discrete sine-Gordon system are spectrally unstable. This is in contrast with more conventional spatially discrete systems, whose breathers…
Nonlinear interaction between normal modes dramatically affects energy equipartition, heat conduction and other fundamental processes in extended systems. In their celebrated experiment Fermi, Pasta and Ulam (FPU, 1955) observed that in…
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…
We consider a nonlinear chain of coupled oscillators, which is a direct generalization of the classical FPU lattice and exhibits, besides the usual nearest neighbor interaction, also next-to-nearest neighbor interaction. For the case of…
We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract…
This paper is concerned with breather solutions of a radially symmetric curl-curl wave equation with double power nonlinearity. By considering the solutions with a special form, we obtain a family of ordinary differential equations (ODEs)…
We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between…
An enhancement of localized nonlinear modes in coupled systems gives rise to a novel type of escape process. We study a spatially one dimensional set-up consisting of a linearly coupled oscillator chain of $N$ mass-points situated in a…
We consider the semilinear curl-curl wave equation $s(x) \partial_t^2 U +\nabla\times\nabla\times U + q(x) U \pm V(x) |U|^{p-1} U = 0 \mbox{ for } (x,t)\in \mathbb{R}^3\times\mathbb{R}$. For any $p>1$ we prove the existence of time-periodic…
We study the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam chains at zero and non-zero temperatures. While such breathers are essentially stationary and very long-lived at zero temperature, thermal fluctuations tend to lead to…
We prove existence of real-valued, time-periodic and spatially localized solutions (breathers) of semilinear wave equations $V(x)u_{tt} - u_{xx} = \Gamma(x) |u|^{p-1} u$ on $\mathbb{R}^2$ for all values of $p\in (1,\infty)$. Using tools…
We propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple…
Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i.…
We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale…
Using two methods we show that a quantized discrete breather in a 1-D lattice is stable. One method uses path integrals and compares correlations for a (linear) local mode with those of the quantum breather. The other takes a local mode as…
We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a)…
We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes,…