On the formation of envelope solitons with tube ended by spherical beads

In this paper it is suggested the possibility of using a simple device to explore the propagation of short transverse perturbations in specimens of three linearly aligned elements (bead, tube and bead). By using time signal analysis and frequency spectroscopy some properties of the transmitted wave packets are experimentally analyzed in the acoustic domain. It is clearly demonstrated that the shape and the velocity of propagation of the waves do not change with distance. The amplitude may vary depending on the dissipation effect. These properties allow us to identify the wave packets as “envelope solitons”. The influence of the elasticity of these materials composing the beads and the tube on the generation of envelope solitons is also investigated.     

Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion

Abstract

The vector-coupled nonlinear Schrödinger equation, which can be applied to describe the propagation of Thirring optical solitons in birefringent ?bers with Kerr law nonlinearity, detuning, intermodal dispersion and spatiotemporal dispersion, has been studied analytically. By means of the complex envelope function ansatz, exact Thirring bright-dark combosolitons are reported, and the properties of these solitons are discussed.     

Envelope solitons of electromagnetic spin waves in an artificial layered multiferroic

The nonlinear wave properties of an artificial multiferroic medium consisting of a ferroelectric layer and a ferromagnetic layer have been studied. The simultaneous effect of wave nonlinearities of both layers on the formation and propagation of envelope solitons has been analyzed. It has been shown that bright envelope solitons of electromagnetic spin waves can appear in such a medium owing to the wave nonlinearity of ferroelectric layer. In order to confirm the theoretical results, the coefficients of the nonlinear Schrödinger equation have been calculated and this equation has been solved numerically.     

Diffraction effects on soliton propagation

An averaged-Lagrangian method is used to analyze diffraction effects on propagation of solitons of various types in homogeneous media. It is shown that diffraction can counteract the self-focusing of dark and gray envelope solitons described by the nonlinear Schrödinger equation and solitons described by the Korteweg-de Vries equation when the soliton intensities do not exceed certain values. Conversely, diffraction enhances the self-focusing of dark and gray envelope solitons described by the modified Korteweg-de Vries equation, kinks described by the sine-Gordon equation, and domain walls in the u 4 model, which is explained by mutual correlation between transverse and longitudinal soliton dynamics. Critical parameters that determine soliton stability with respect to self-focusing are found for several models.     

Formation of envelope solitons of spin-wave packets propagating in thin-film magnon crystals

The formation of light envelope solitons has been experimentally observed under the pulsed excitation and propagation of radio-frequency spin-wave packets in a magnon crystal, a periodic magnetic film structure. The magnon crystal has been fabricated from a thin single-crystal yttrium iron garnet (YIG) film. The envelope solitons have been excited at frequencies corresponding to the edges of the Bragg-resonance-induced band gaps of the spin-wave spectrum of the magnon crystal. A theoretical explanation of the observed phenomenon has been proposed with the use of the numerical simulation of the formation of solitons based on the nonlinear Schrödinger equation.     

非线性静磁表面波的传播特性

将文献[4]的理论结果加以推广,用微扰理论导出了微波场作用下铁磁材料的动态非线性磁化强度的各阶近似表达式。严格分析了在波矢k与外偏置磁场H₀成任意角度时非线性静磁表面波的传播特性。证明了静磁表面波在任何传播方向上都不能演化为静磁孤子。 关键词：     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Observation of the amplification of spin-wave envelope solitons in ferromagnetic films by parallel magnetic pumping

The propagation of envelope solitons of microwave-frequency spin waves in a spatially periodic field oriented parallel to the magnetic pump has been investigated experimentally. In a pulsed pumping regime with amplitude much greater than the threshold for parametric excitation of spin systems, amplification of spin-wave envelope solitons exceeding their natural damping was obtained. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 346–350 (10 September 1997)     

Envelope solitons in acoustically dispersive vitreous silica

Acoustic radiation-induced static strains, displacements, and stresses are manifested as rectified or 'dc' waveforms linked to the energy density of an acoustic wave or vibrational mode via the mode nonlinearity parameter of the material. An analytical model is developed for acoustically dispersive media that predicts the evolution of the energy density of an initial waveform into a series of energy solitons that generates a corresponding series of radiation-induced static strains (envelope solitons). The evolutionary characteristics of the envelope solitons are confirmed experimentally in Suprasil W1 vitreous silica. The value (- 11.9 ± 1.43) for the nonlinearity parameter, determined from displacement measurements of the envelope solitons via a capacitive transducer, is in good agreement with the value (- 11.6 ± 1.16) obtained independently from acoustic harmonic generation measurements. The agreement provides strong, quantitative evidence for the validity of the model.     

Observation of spin-wave envelope solitons in periodic magnetic film structures

The formation and propagation of light and dark microwave spin-wave envelope solitons in a periodic magnetic film structure have been observed. The periodic structure was manufactured on the basis of the single-crystal film of iron-yttrium garnet and a lattice of copper strips placed on the surface of the film perpendicularly to the propagation direction of carrying spin waves. The solitons are generated at frequencies corresponding to the band gap in the spectrum of the spin waves of the periodic structure, which is due to the first Bragg resonance.     

Theoretical investigation of an acoustic wave in molecular magnets via electromagnetically induced transparency

Using the Schrödinger-Maxwell equations, we theoretically investigate the propagation properties of a transverse acoustic wave in a crystal of molecular magnets in the presence of two strong ac resonant magnetic fields and a weak acoustic wave. The acoustic wave can freely propagate in the magnetic molecule medium (under appropriate conditions) due to quantum interference. Furthermore, using the slowly varying envelope approximation, we discuss the propagation equation of the acoustic wave, which includes the high order nonlinear term. The results show that a crystal of molecular magnets can support the propagation of acoustic wave solitons via electromagnetically induced transparency. We also obtain the analytical expressions for the phase shift and absorption coefficient of the acoustic wave within certain parameters.     

Electrostatic dust-acoustic envelope solitons in an electron-depleted plasma

A standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust-acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron-depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super-thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super-thermality of the positive ions, etc.) have rigorous impact to recognize the stability conditions of dust-acoustic waves. The present study is useful for understanding the mechanism of the formation of dust-acoustic envelope solitons associated with dust-acoustic waves in the laboratory and space environments.     

Pulse modes for the magnetostatic-wave envelope in a magnetically coupled two-layer structure

The propagation of the envelope of direct bulk magnetostatic-wave pulses in a structure consisting of two magnetically coupled films separated by a nonmagnetic layer is studied. It is found that mode coupling substantially affects the dispersion properties of the structure, thereby determining the excited pulse modes in many respects and resulting in their dependence on the type of excitation of the structure. The conditions for the formation of solitons in magnetically coupled structures are derived. The dynamics of pulses with different initial profiles and lengths is investigated. The appearance of pulses with pulsing side regions is established.     

Interaction of (1+1)-dimensional dipole solitons in optical lattice

The interaction between two (1+1)-dimensional dipole solitons in a weak modulation lattice is studied numerically. Two unstable dipole solitons can form the bound state, and their propagation can be stabilized due to their mutual interaction. The propagation patterns with the interaction are dependent on the interval, relative phase, and input energy of the two dipole solitons. The two poles of the dipole soliton exchanges their energy after the interaction. Under the proper conditions, the interaction force between the two dipole solitons exhibits some properties similar to those between two molecules.     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Soliton envelope modulation instability and amplification in a semiconductor with striction-type electromechanical coupling

Modulation instability is considered for an electromagnetic wave incident on a ferroelectric semiconductor. The instability conditions coincide with those for drift and parametric sound excitation by an external electric field. Electrosound envelope solitons can exist in such a semiconductor. A study is made on how a steady electric field affects the envelope soliton propagation, and an amplification criterion is derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 93–97, November, 1990.     

Axisymmetric Nonlinear Modulated Waves in a Cylindrical Shell

A quasi-hyperbolic equation is derived that simulates the axisymmetric propagation of bending waves in a cylindrical shell, which interacts with a nonlinearly elastic medium. With the correct asymptotic procedure, the study of a wave process reduces to analysis of a nonlinear Schrödinger equation. It is established that the development of modulation instability requires a “soft” nonlinearity of the medium surrounding the shell. Operating modes that allow the propagation of stable light envelope solitons are revealed.