Related papers: Energy thresholds for discrete breathers
We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different…
The existence of breathers (time-periodic and spatially localized lattice vibrations) is well established for i) systems without acoustic phonon branches and ii) systems with acoustic phonons, but also with additional symmetries preventing…
We study the formation of breathers in multi-dimensional lattices with long-range interactions. By variational methods, the exact relationship between various parameters (dimension, nonlinearity, nonlocal parameter $\alpha$) that defines…
Quantum breathers are studied numerically in several electron-phonon coupled finite chain systems, in which the coupling results in intrinsic nonlinearity but with varying degrees of nonadiabaticity. As for quantum nonlinear lattice…
Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in $d$ spatial dimensions imposing anti de…
We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay.…
Nonlinear networks can host spatially compact time periodic solutions called compact breathers. Such solutions can exist accidentally (i.e. for specific nonlinear strength values) or parametrically (i.e. for any nonlinear strength). In this…
Qualitative information about breather initial profiles in the weak coupling limit of a chain of identical one-dimensional anharmonic oscillators is found by studying the linearized equations of motion at a one-site breather. In particular,…
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 question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier…
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…
The Discrete NonLinear Schr\"odinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic…
Breathers may be mobile close to an instability threshold where the frequency of a pinning mode vanishes. The translation mode is a marginal mode that is a solution of the linearized (Hill) equation of the breather which grows linearly in…
In the present chapter, we explore the possibility of a Frenkel-Kontorova (discrete sine-Gordon) model to bear interactions that decay algebraically with space, inspired by the continuum limit of the corresponding fractional derivative. In…
Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…
We touch upon the wide topic of discrete breather formation with a special emphasis on the the $\phi^4$ model. We start by introducing the model and discussing some of the application areas/motivational aspects of exploring time periodic,…
We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of…
We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for the…
Magnetic metamaterials composed of split-ring resonators or $U-$type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array…
Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the…