Soliton-like Waves Research Articles

Electronic and mechanical realizations of one-way coupling in one and two dimensions

One-way or unidirectional coupling is a striking example of how topological considerations--the parity of an array of multistable elements combined with periodic boundary conditions--can qualitatively influence dynamics. Here we introduce a simple electronic model of one-way coupling in one and two dimensions and experimentally compare it to an improved mechanical model and an ideal mathematical model. In two dimensions, computation and experiment reveal richer one-way coupling phenomenology: in media where two-way coupling would dissipate all excitations, one-way coupling enables solitonlike waves to propagate in different directions with different speeds.

Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma

The propagation of large amplitude ion-acoustic solitary waves (IASWs) in a fully relativistic plasma consisting of cold ions and ultra-relativistic hot electrons and positrons is investigated using the Sagdeev pseudopotential method in a relativistic hydrodynamics model. The effects of streaming speed of the plasma fluid, thermal energy, positron density, and positron temperature on large amplitude IASWs are studied by analysis of the pseudopotential structure. It is found that in regions in which the streaming speed of the plasma fluid is larger than that of the solitary wave, by increasing the streaming speed of the plasma fluid, the depth and width of the potential well increase, resulting in narrower solitons with larger amplitude. This behavior is opposite to the case where the streaming speed of the plasma fluid is less than that of the solitary wave. On the other hand, an increase in the thermal energy results in wider solitons with smaller amplitude, because the depth and width of the potential well decrease in that case. Additionally, the maximum soliton amplitude increases and the width becomes narrower as a result of an increase in positron density. It is shown that varying the positron temperature does not have a considerable effect on the width and amplitude of IASWs. The existence of stationary soliton-like arbitary amplitude waves is also predicted in fully relativistic electron-positron-ion (EPI) plasmas. The effects of streaming speed of the plasma fluid, thermal energy, positron density, and positron temperature on these kinds of solitons are the same for large amplitude IASWs.

New soliton-like solutions and compacton-like periodic wave solutions of parametric type to a nonlinear dispersive equation

In this paper, by using the integral bifurcation method, we study a nonlinear dispersive equation. Some new soliton-like solutions and some compacton-like periodic wave solutions are obtained. Their dynamic characters are investigated and the profiles are given by the mathematical software Maple. From the graphs of some soliton-like solutions, we find that their profiles are transformable.

Propagation and interaction of nonlinear waves in a liquid with gas bubbles

The propagation and interaction of nonlinear solitonlike waves in a liquid with gas bubbles are considered using the Nakoryakov-Pokusaev-Shreiber two-wave equation. It is shown that these waves exist within the “opacity” window for linear waves. The interaction of such waves propagating in opposite directions may lead to their splitting into secondary localized waves.

ChemInform Abstract: Applications and Trends in Electrochemiluminescence

AbstractReview: 322 refs.

Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves

Under investigation in this paper, with symbolic computation, is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves travelling in two horizontal directions with varying depth. Connection between the vcvB model and a variable-coefficient Broer-Kaup (vcBK) system is revealed under certain constraints. By means of the N-fold Darboux transformation for the vcBK system, odd-soliton-like solutions in terms of the Vandermonde-like determinant for the vcvB model are derived. Dynamics of those solutions is analyzed graphically, on the three-parallel solitonic waves, head-on collisions, double structures, and inelastic interactions. It is reported that the shapes of the soliton-like waves and separation distance between them depend on the spectrum parameters and the variable coefficients affect the velocities of the waves. Our results could be helpful in interpreting certain nonlinear wave phenomena in fluid dynamics.

Model of periodic superstructure formation induced by mobile defects on a semiconductor surface

A model for forming a periodic superstructure on a semiconductor surface with mobile defects is proposed. It is shown that a self-organized system of such defects could lead to considerable modulation of incommensurate phase parameters in near-surface layers under the conditions of defect interaction with an incommensurate displacement wave. This type of defect system could induce a substantial energy decrease for the incommensurate phase and its additional stabilization on the one hand, and an increase in modulation amplitude that might be accompanied by a soliton-like nonsinusoidal incommensurate displacement wave on the other. The model allows us to explain the experimental results regarding the periodic superstructure discovered by G.V. Benemanskaya et al. on the surface of a GaN semiconductor. In particular, the model enables us to explain the nature of such superstructures based on the self-organization of mobile neutral triad-type defects, composed of negatively charged (3−) vacancies of the host lattice centers of Ga3+ and surface impurity ions of Cs+ and Ba2+, under conditions of triad interaction with an incommensurate displacement wave.

Propagation of solitary waves in magnetized three-component plasmas

The propagation of nonlinear ion-acoustic waves in magnetized plasma consisting of cold ions, hot electrons and positrons has been studied. It is demonstrated that in the case of weak nonlinearity the ion-acoustic waves are described by the Korteweg–de Vries (K-dV) equation. The influence of finite positron density and temperature and external magnetic field on the properties of soliton-like waves is discussed.

Generation of Three-Dimensional Fully Nonlinear Water Waves by a Submerged Moving Object

This paper describes a numerical investigation on the generation of three-dimensional (3D) fully nonlinear water waves by a submerged object moving at speeds varied from subcritical to supercritical conditions in an unbounded fluid domain. Considering a semispheroid as the moving object, simulations of the time evolutions of 3D free-surface elevation and flow field are performed. The present 3D model results are found to agree reasonably well with other published vertical two-dimensional (2D) and quasi-3D numerical solutions using Boussinesq-type models. Different from the 2D cases with near critical moving speeds, the 3D long-term wave pattern suggests that in addition to the circularly expanded upstream advancing solitonlike waves, a sequence of divergent and transverse waves are also developed behind the moving object. The velocity distributions and associated fluid-particle trajectories at the free-surface and middle layers are presented to show the 3D feature of the motion. The results under various vertical positions (referred as gap) of a moving object are also compared. It is found the gap has shown a substantial influence on the generated waves, especially in the wake region, when an object moves at a near critical or subcritical speed. However, the results under the case with a high supercritical moving speed indicate the gap has a negligible effect on the generated upstream and downstream waves.

Cross Soliton-Like Waves for the (2+1)-Dimensional Breaking Soliton Equation

We construct a two-soliton-like solution for the (2+1)-dimensional breaking soliton equation. The obtained solution contains two arbitrary functions and hence can model various cross soliton-like waves including the two-solitary waves. We show the evolution of some special cross soliton-like waves diagrammatically.

Simulation of processes of dynamic deformation in a structured geophysical medium with elastic - plastic interaction of structure elements

The computer simulation of the process of nonlinear wave propagation in a structured geophysical medium with elastic-plastic interaction between the structure elements is conducted. It is found that during the wave propagation in a chain of the discrete elements its amplitude decays to the threshold value, when the interaction between the elements becomes elastic, and then the wave is transformed into a soliton-like wave with the threshold amplitude. The deformation diagrams of the massifs at different plastic threshold values are plotted. It is demonstrated that a decrease of the plastic threshold results in an increase of the dissipative properties.

Applications and trends in electrochemiluminescence

Electrochemiluminescence (ECL) is chemiluminescence triggered by electrochemical techniques. More than 150 ECL assays with remarkably high sensitivity and extremely wide dynamic range are currently available, and accounts for hundreds of millions of dollars in sales per year. The recent development of ECL is particularly rapid. After a brief introduction to ECL, this critical review presents the active and/or emerging areas of ECL research as well as new applications and phenomena of ECL, such as light-emitting electrochemical cell, wireless electrochemical microarray using ECL as photonic reporter, high throughput analysis, aptasensors, immunoassays and DNA analysis, ECL of nanoclusters and carbon nanomaterials, ECL imaging techniques, scanning ECL microscopy, colorimetric ECL sensor, surface plasmon-coupled ECL, electrostatic chemiluminescence, soliton-like ECL waves, ECL investigation of molecular interaction, and single molecule detection. Finally, some perspectives on this rapidly developing field are discussed (322 references).

Traveling waves of step density and solution supersaturation in the assigned diffusion layer thickness model of step bunching

Step bunching in crystal growth from solutions is investigated theoretically in the approximation of nonstationary mass transfer in a diffusion layer of assigned thickness. It is shown that this model is described by a set of equations including a diffusion equation for a diffusion layer, a one-dimensional step motion equation, the boundary conditions relating these equations, and the boundary condition at the diffusion layer boundary. This set of equations has solutions in the form of coupled traveling periodical and soliton-like waves of density steps n and relative supersaturation σ on the growing surface and in volume of the diffusion layer. The parameters obtained for traveling n and σ agree with experimental data on step bunches in KDP crystal growth.

Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation

In this paper, by using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by Mathematical software.

Peculiarities of periodic and aperiodic energy-exchange regimes in the cascade quasi-synchronous parametric frequency conversion

The domains of existence and peculiarities of exact analytic solutions of the problem of quasi-synchronous interaction of four plane collinear monochromatic waves — modes in a quadratically nonlinear medium during cascade frequency conversion are analysed. It is shown that the unusual types of multicomponent cnoidal and solitary soliton-like waves (of periodic and aperiodic energy-exchange regimes) are realised. Two of the four components of the latter are proportional to the real and imaginary parts of the well-known Lorentzian dependence, which is commonly used to describe the dispersion of contributions from resonance transitions to the complex permittivity in the case of homogeneous line broadening.

Novel Asymptotic SolitonWaves for the Nonlinear Schrödinger Equation with Varying Gain/Loss and Frequency Chirping

Abstract This paper analysis spatial asymptotic waves propagation in nonuniform optical fiber. It finds an appropriate transformation such that the nonlinear variable-coefficient Schr¨odinger equation transform into the nonlinear Schr¨odinger equation with varying gain/loss and frequency chirping. It obtains solitonlike and periodic self-similar asymptotic waves by using the transformation. We analyze the evolution properties of some novel self-similar solutions. In addition, the nature of our self-similar asymptotic wave hints to the possibility of designing optical amplifier and focusing of spatial waves to overcome inevitable energy losses while performing in the optical nonlinear media.

Soliton-like lamb waves

The velocity and polarization of acoustic Lamb waves, propagating in the directions of elastic symmetry of single-layer and double-layer anisotropic media at vanishingly low frequencies (soliton-like waves), are investigated. The method of fundamental matrices is used to construct solutions. The conditions for soliton-like Lamb waves to exist are analysed.

Nonlinear dynamics of optical pulses in fibreswith a travelling refractive-index-change wave

Dynamics of soliton-like wave packets in fibreswith a travelling refractive-index-change wave is studied. It isshown that both a soliton-like propagation regime of a pulseand a self-compression regime in the region of normal groupvelocity dispersion are possible. It is also shown that in thecase of a copropagating or counterpropagating pulse andoptically inhomogeneous wave nonreciprocal effects appear.

Theoretical and experimental study of energy dissipation in the course of strain localization in iron

Plastic strain localization is studied with the use of a high-sensitivity infrared camera. Plastic strain localization in iron is demonstrated to be accompanied by the emergence of heat waves and their propagation over the sample surface. Constitutive equations that describe the energy balance in the material under plastic strains are derived, and the plastic flow of iron is analyzed. The results of research are compared with the data obtained by infrared scanning. The proposed model of strain localization in the form of soliton-like waves (phase triggering waves) is demonstrated to agree with the kinetics of temperature waves characterizing dissipation inherent in the development of plastic deformation.

Mass-Transport and Step Bunching in Crystal Growth from Solutions

Step bunching in crystal growth from solutions is investigated theoretically in the approximation of nonstationary mass transport in diffusion layer of assigned thickness. It is shown that this model is described by a set of equations, including a diffusion equation for a diffusion layer, a one-dimensional step motion equation, the boundary conditions relating these equations, and the boundary condition at the diffusion layer boundary. This set of equations has solutions in the form of coupled traveling periodical and soliton-like waves of density steps n and relative supersaturation σ x on the growing surface. The amplitude, the wavelength, and the propagation velocity depend on the degree of deviation of growth parameters from “equilibrium” ones for which the bunch amplitude tends to zero. The parameters obtained for traveling n and σ x agree with experimental data on step bunches in potassium dihydrogen phosphate, KH2PO4 (KDP) crystal growth.