Probability of breaking of the PJ symmetry at collision between breathers with random phases in the model of a PJ symmetric planar coupler

The interaction between breathers has been studied in the model of a nonlinear plane PJ-symmetric coupler. It has been shown that the dynamics of the interaction depends significantly on the relative phase of the breathers. The probability of breaking of the PJ symmetry in the collision of breathers having random initial phases has been estimated for various sets of parameters of the model and breathers. Various scenarios of collision of breathers have been described.     

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study the collisions of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions some possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a bound state. Breather annihilation has never been observed.     

Highly symmetric discrete breather in a two-dimensional Morse crystal

It has been shown recently that a moving discrete breathers localized in one close-packed atomic row can be excited in a two-dimensional monoatomic crystal with Morse interaction. In this work, a motionless discrete breathers having the threefold symmetry axis has been excited in the same crystal. The initial conditions for the excitation of such discrete breathers are set by the superposition of a bell-shaped function on a planar nonlinear phonon mode with the wave vector lying at the edge of the Brillouin zone. In addition, the displacement of the centers of atomic oscillations from the center of the discrete breathers owing to the asymmetry of the Morse potential is taken into account. The results obtained make it possible to approach the search for highly symmetric discrete breathers in three-dimensional crystals.     

Interaction of two-dimensional electromagnetic breathers in an array of carbon nanotubes

The propagation and interaction of two-dimensional bipolar electromagnetic pulses in an array of semiconducting carbon nanotubes have been investigated. The electromagnetic field in the array of carbon nanotubes has been described by the Maxwell’s equations reduced to the non-one-dimensional wave equation. The initial distribution of the field has been specified in the form of approaching breathers bounded by a Gaussian profile in the plane perpendicular to the pulse propagation direction. The numerical solution of the wave equation has revealed the possibility of stable propagation of breathers in the array of carbon nanotubes. It has been found that the interaction of electromagnetic breathers in the array of semiconducting carbon nanotubes has a character of quasi-elastic collisions.     

Spontaneous excitation of discrete breathers in crystals with the NaCl structure at elevated temperatures

The density of phonon states at various temperatures has been calculated for crystals with the NaCl structure with equal and strongly differing weights of anions and cations. It has been shown that, in the crystal with a considerable difference in the weights of components, a wide band gap exists in the spectrum of phonon states, which leads to spontaneous excitation of nonlinear localized vibrational modes??gap discrete breathers having frequencies inside the band gap, if the temperature is sufficiently high. It has been found that the peak of the density of phonon states lying above the spectrum of linear vibrations appears at elevated temperatures, which can indicate the existence of discrete breathers with corresponding frequencies. It has been noted that, previously, the existence of gap discrete breathers in the NaI crystal at 555 K was shown experimentally. The presented results bring up the question of the theoretical justification and experimental observation of the breathers with frequencies above the phonon spectrum.     

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry's theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.     

On symmetric breather collisions in lattices with saturable nonlinearity

Symmetric collisions of two discrete breathers in the lattice with saturable nonlinearity are investigated. The strong correlation of the collision properties and the parameters of colliding breathers (power, velocity, and phase difference), lattice parameters and position of the collision point is found. This is related to the internal structure of the colliding breathers and energy exchange with the phonon background. The type of collision changes from elastic to the inelastic (the breathers merging, multi-bounce interactions, breather creation etc.) with the increasing of the colliding breather power. Collision of high power breathers always results in the breather fusion. The elastic and inelastic collisions are related to the periodic and quasi-periodic colliding breathers, respectively.     

Moving breather collisions in Klein-Gordon chains of oscillators

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of oscillators. The on-site potentials are: the asymmetric and soft Morse potential, the symmetric and soft sine-Gordon potential and the symmetric and hard φ⁴ potential. The simulation of a collision begins generating two identical moving breathers traveling with opposite velocities, they are obtained after perturbing two identical stationary breathers which centers are separated by a fixed number of particles. If this number is odd we obtain an on-site collision, but if this number is even we obtain an inter-site collision. Apart from this distinction, we have considered symmetric collisions, if the colliding moving breathers are vibrating in phase, and anti-symmetric collisions, if the colliding moving breathers are vibrating in anti-phase. The simulations show that the collision properties of the three chains are different. The main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities, and a stationary breather trapped at the collision region; breather generation without trapping, with the appearance of new moving breathers with opposite velocities; breather trapping at the collision region, without the appearance of new moving breathers; and breather reflection. For each Klein-Gordon chain, the collision outcomes depend on the lattice parameters, the frequency of the perturbed stationary breathers, the internal structure of the moving breathers and the number of particles that initially separates the stationary breathers when they are perturbed.     

Quantum Breathers in an Anisotropic Ferromagnetic Heisenberg Chain with Biquadratic Exchange Interaction

Based on the Hartree approximation and the semidiscrete multiple-scale method, quantum breathers in an anisotropic ferromagnetic Heisenberg chain with biquadratic exchange interaction are predicted analytically. The existence condition of quantum breathers is obtained, and the properties of quantum breathers are analyzed. Moreover, it is shown that the energy of such quantum breathers is quantized.     

Influence of elastic strain on the density of phonon states and characteristics of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure

Appreciable elastic strain may considerably change the physical properties of crystals. This effect underlies the elastic stress technology, which has been intensively developed in recent years. The influence of elastic strain on the density of phonon states and on the properties of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure and a considerable difference between the anion and cation masses is studied using the molecular dynamics method. A number of crystal straining modes are considered. It is shown that the shear components of the strain tensor may significantly change the density of phonon states but slightly influence the frequencies of discrete breathers. Compression (tensile) strains raise (lower) the frequency of discrete breathers with a respective polarization.     

Discrete breathers

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. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurrence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices — quantum breathers.Finally we will formulate a new conceptual approach capable of predicting whether discrete breathers exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.     

Discrete breathers — Advances in theory and applications

Nonlinear classical Hamiltonian lattices exhibit generic solutions — discrete breathers. They are time-periodic and (typically exponentially) localized in space. The lattices have discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. We will introduce the concept of these localized excitations and review their basic properties including dynamical and structural stability. We then focus on advances in the theory of discrete breathers in three directions — scattering of waves by these excitations, persistence of discrete breathers in long transient processes and thermal equilibrium, and their quantization. The second part of this review is devoted to a detailed discussion of recent experimental observations and studies of discrete breathers, including theoretical modelling of these experimental situations on the basis of the general theory of discrete breathers. In particular we will focus on their detection in Josephson junction networks, arrays of coupled nonlinear optical waveguides, Bose–Einstein condensates loaded on optical lattices, antiferromagnetic layered structures, PtCl based single crystals and driven micromechanical cantilever arrays.     

Enhanced mobility of high-frequency discrete breathers in a monatomic chain with odd anharmonicity

The mobility of high-frequency discrete breathers in monatomic chains with nonlinear interatomic potentials of the nearest neighbors is considered. It was found that the odd (cubic and fifth) anharmonicity strongly affects the mobility of breathers, sharply increasing the distance that it propagates without being trapped. It was also found that the correctly chosen fifth anharmonicity leads to an inversion of stability between the bond-centered and site-centered breathers and to the low-radiative propagation of discrete breathers along the chain.     

Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of mobile breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a “symmetry breaking” can be observed, which we show to be an numerical artifact.     

Dissipative discrete breathers: periodic,quasiperiodic, chaotic,and mobile

The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations.     

The degeneration of the breathers for the BKP equation

In this paper, by the complexification of the wave number of the soliton given by the Hirota bilinear method, we get the breather solutions. Lumps of the BKP equations are constructed by full degeneration of the breathers, i.e., the limit of infinitely large period of the breathers. The localization characters of the 1-order lump by contour line method are studied analytically. The partial degeneration of the breathers yields hybrid solutions including soliton, lump and breathers.     

Two-Dimensional Discrete Gap Breathers in a Two-Dimensional Diatomic β Fermi--Pasta--Ulam Lattice

We study the existence of two-dimensional discrete breathers in a two-dimensional face-centred square lattice consisting of alternating light and heavy atoms, with nearest-neighbour coupling containing quartic soft or hardnonlinearity. This study is focused on two-dimensional breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of existence of two-dimensional gap breathers by using the numerical method, the local anharmonicity approximation and the rotating wave approximation. We obtain six types of two-dimensional gap breathers, i.e., symmetric, mirror-symmetric and asymmetric, no matter whether the centre of the breather is on a light or a heavy atom.     

Low-frequency breathers in polyethylene crystal

It is shown both analytically and numerically that three-dimensional low-frequency (acoustic) breathers identified as localized coupled bend and twist nonlinear waves can exist in polyethylene (PE) crystal. Their motion along the chain is accompanied by the simultaneous excitation of both (“zig” and “zag”) sub-chains forming PE macromolecule.In the region of a breather one can observe intensive out-of-plane motion of carbon atoms and relatively small displacements in the plane of the zigzag. In spite of this smallness, the “secondary” nonlinear effects turn out to be crucial for the existence of breathers.Both the existence and stability of low-frequency breathers in free motion are confirmed by computer simulation, using the Molecular Dynamics (MD) procedure. The stability of breathers with respect to thermal excitations as well as to mutual collisions and collisions with optical breathers is also discussed. We study also the breathers’ formation in different conditions. It turns out that the frequencies and extensions of the breathers can be varied in very narrow regions predicted by our analytical solution.     

Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice

We study the existence and stability of two-dimensional discrete breathers in a two-dimensionai discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling. Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential （soft or hard）, the interaction potential （attractive or repulsive） and the center of the two-dimensional gap breathers （on a light or a heavy atom）.     

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell’s mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schro¨dinger equation.