Related papers: Some breathers and multi-breathers for FPU-type ch…
Breather stability and longevity in thermally relaxing nonlinear arrays depend sensitively on their interactions with other excitations. We review the relaxation of breathers in Fermi-Pasta-Ulam arrays, with a specific focus on the…
We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is…
We numerically realize breather gas for the focusing nonlinear Schr\"odinger equation. This is done by building a random ensemble of N $\sim$ 50 breathers via the Darboux transform recursive scheme in high precision arithmetics. Three types…
We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting…
Existence of large-amplitude time-periodic breathers localized near a single site is proved for the discrete Klein--Gordon equation, in the case when the derivative of the on-site potential has a compact support. Breathers are obtained at…
We prove the existence of discrete breathers (time-periodic, spatially localized solutions) in weakly coupled ferromagnetic spin chains with easy-axis anisotropy. Using numerical methods we then investigate the continuation of discrete…
We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice $\mathbb{Z}$. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively.…
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered…
Inspired by the experimental results of Cuevas et al. (Physical Review Letters 102, 224101 (2009)), we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a…
We consider the Hamiltonian version of a $\cal PT$-symmetric lattice that describes dynamics of coupled pendula under a resonant periodic force. Using the asymptotic limit of a weak coupling between the pendula, we prove the nonlinear…
The Fermi-Pasta-Ulam (FPU) paradox was observed fifty years ago. The surprising finding was a localization of energy in the reciprocal q-space of a model with discrete translational invariance, despite the presence of interaction between…
The problem of showing the existence of localised modes in nonlinear lattices has attracted considerable efforts from the physical but also from the mathematical viewpoint where a rich variety of methods has been employed. In this paper we…
We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1+1) dimensions. The main motivation of our study is to test the ideas behind the…
In the present work, we develop a systematic examination of the existence, stability and dynamical properties of a discrete breather at the interface between a diatomic and a monoatomic granular chain. We remarkably find that such an…
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry.…
Dynamics of array of coupled self-excited oscillators is considered. Model of Franklin bell is adopted as a mechanism for the self-excitation. The model allows derivation of exact analytic solutions for discrete breathers (DBs), and…
We numerically study the existence of travelling breathers in Klein-Gordon chains, which consist of one-dimensional networks of nonlinear oscillators in an anharmonic on-site potential, linearly coupled to their nearest neighbors.…
We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are $H^2(\mathbb{R})$ stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov…
After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU) conservative system of $N$ nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU…
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)…