Bose-Einstein condensation (BEC) has been observed in a dilute gas of sodium atoms. A Bose-Einstein condensate consists of a macroscopic population of the ground state of the system, and is a coherent state of matter. In an ideal gas, this phase transition is purely quantum-statistical. The study of BEC in weakly interacting systems which can be controlled and observed with precision holds the promise of revealing new macroscopic quantum phenomena that can be understood from first principles.

Bose-Einstein condensation in a gas of sodium atoms

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 occurence 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 aproach capable of predicting whether discrete breather 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

Discrete breathers — Advances in theory and applications

In the course of the past several years, a new level of understanding has been achieved about conditions for the existence, stability, and generation of spatiotemporal optical solitons, which are nondiffracting and nondispersing wavepackets propagating in nonlinear optical media. Experimentally, effectively two-dimensional (2D) spatiotemporal solitons that overcome diffraction in one transverse spatial dimension have been created in quadratic nonlinear media. With regard to the theory, fundamentally new features of light pulses that self-trap in one or two transverse spatial dimensions and do not spread out in time, when propagating in various optical media, were thoroughly investigated in models with various nonlinearities. Stable vorticity-carrying spatiotemporal solitons have been predicted too, in media with competing nonlinearities (quadratic–cubic or cubic–quintic). This article offers an up-to-date survey of experimental and theoretical results in this field. Both achievements and outstanding difficulties are reviewed, and open problems are highlighted. Also briefly described are recent predictions for stable 2D and 3D solitons in Bose–Einstein condensates supported by full or low-dimensional optical lattices.

https://iopscience.iop.org/article/10.1088/1464-4266/7/5/R02/pdf

Spatiotemporal optical solitons

The nondestructive assessment of the damage that occurs in components during service plays a key role for condition monitoring and residual life estimation of in-service components/structures. Ultrasound has been widely utilized for this; however most of these conventional methods using ultrasonic characteristics in the linear elastic region are only sensitive to gross defects but much less sensitive to micro-damage. Recently, the nonlinear ultrasonic technique, which uses nonlinear ultrasonic behavior such as higher-harmonic generation, subharmonic generation, nonlinear resonance, or mixed frequency response, has been studied as a positive method for overcoming this limitation. In this paper, overall progress in this technique is reviewed with the brief introduction of basic principle in the application of each nonlinear ultrasonic phenomenon.

Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review

The supersonic motion of a crowdion. The one-dimensional model with nonlinear interaction between the nearest neighbours

Self-localization of vibrations in a one-dimensional anharmonic chain

The soliton states localized at a point defects are investigated by using the nonlinear Schrodinger equation for various signs of the nonlinearity and for different types of defects. The quantum interpretation of these nonlinear localized modes is given in terms of bound states of a large number of Bose particles. The dynamic properties and stability of these states for different types of interaction between elementary excitations with one another and with the defect are investigated. The boundaries of the region of existence and stability of “impurity” solitons are determined depending on the “intensity” of the defect, and the frequency of small oscillations of a soliton near the defect is calculated.

Dynamics and stability of localized modes in nonlinear media with point defects

Solitary acoustic pulses can propagate along the surface of a coated homogeneous and inhomogeneous medium It is shown how these nonlinear surface acoustic waves evolve out of initial pulselike conditions generated by pulsed laser excitation and how they can be monitored by optical detection The solitary pulse shapes at the surface are computed on the basis of an evolution equation with nonlocal nonlinearity They depend on the anisotropy of the substrate Various approaches for the derivation of the evolution equation from nonlinear elasticity theory are critically compared The behavior of the solitary pulses in collisions is investigated and is found to strongly depend on the linear dispersion law The nontrivial depth dependence of these solitary pulses is also analyzed

/pdf/solitary-surface-acoustic-waves-4n5eo1xs5d.pdf

Alexander S. Kovalev

Papers

The supersonic motion of a crowdion. The one-dimensional model with nonlinear interaction between the nearest neighbours

Self-localization of vibrations in a one-dimensional anharmonic chain

Dynamics and stability of localized modes in nonlinear media with point defects

Solitary surface acoustic waves.

Dynamical and topological solitons in a ferromagnet