Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete bright breathers are well known phenomena. They are localized excitations that consist of a few excited oscillators in a lattice and the rest of them having very small amplitude or none. In this paper we are interested in the opposite kind of localization, or discrete dark breathers, where most of the oscillators are excited and one or a few units of them have very small amplitude. We investigate using band analysis, Klein--Gordon lattices at frequencies not close to...

We explore dynamics of discrete breathers and multi-breathers in finite one-dimensional chain. The model involves parabolic on-site potential with rigid constraints and linear nearest-neighbor coupling. The rigid non-ideal impact constraints are the only source of nonlinearity and damping in the model. The model allows derivation of exact analytic solutions for the breathers and multi-breathers with arbitrary set of localization sites, both in conservative and forced-damped s...

Consider an infinite chain of masses, each connected to its nearest neighbors by a (nonlinear) spring. This is a Fermi-Pasta-Ulam-Tsingou lattice. We prove the existence of traveling waves in the setting where the masses alternate in size. In particular we address the limit where the mass ratio tends to zero. The problem is inherently singular and we find that the traveling waves are not true solitary waves but rather "nanopterons", which is to say, waves which asymptotic at ...

We propose a new mechanism of long-range coupling to excite low-frequency discrete breathers without the on-site potential. This mechanism is universal in long-range systems irrespective of the spatial boundary conditions, of topology of the inner degree of freedom, and of precise forms of the coupling functions. The limit of large population is theoretically discussed for the periodic boundary condition. Existence of discrete breathers is numerically demonstrated with stabil...

There exists a recent mathematical proof on the existence of small amplitude breathers in FPU systems near the phonon band, which includes a prediction of their amplitude and width. In this work we obtain numerically these breathers, and calculate the range of validity of the predictions, which extends relatively far from the phonon band. There exist also large amplitude breathers with the same frequency, with the consequence that there is an energy gap for breather creation ...

Steadily moving transition (switching) fronts, bringing local transformation, symmetry breaking or collapse, are among the most important dynamic coherent structures. The nonlinear mechanical waves of this type play a major role in many modern applications involving the transmission of mechanical information in systems ranging from crystal lattices and metamaterials to macroscopic civil engineering structures. While many different classes of such dynamic fronts are known, the...

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal ...

Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of discrete breather that exist at the atomic scale in a magnetic solid. Other observations of breathers refer to systems such as Josephson--junction arrays, photonic crystals and optical-switching waveguide arrays. All these observations under...

We consider several breather solutions for FPU-type chains that have been found numerically. Using computer-assisted techniques, we prove that there exist true solutions nearby, and in some cases, we determine whether or not the solution is spectrally stable. Symmetry properties are considered as well. In addition, we construct solutions that are close to (possibly infinite) sums of breather solutions.

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 (multibreathers) are considered. The model is scalar, i.e. each particle can move only parallel to the axis of the chain it belongs to. The model involves symmetric parabolic on-site potential with rigid constraints (the displacement domain ...