Solitary surface waves on a thin plasma layer

In this review we consider the propagation of nonlinear waves in magnetically structured plasmas. We start from studying nonlinear surface waves on magnetic interfaces and give a derivation of the equation governing propagation of these waves in incompressible plasmas. We present the results of a numerical solution of this equation. Then we discuss various generalizations of this equation.We proceed to study slow nonlinear waves in magnetic slabs. We present the Benjamin-Ono equation describing nonlinear slow sausage surface waves in magnetic slabs, and discuss its solutions in the form of algebraic solitons. Then we consider nonlinear slow body waves and write down the governing equation for these waves. We discuss its numerical solution which shows that the evolution of an initial perturbation results in a gradient catastrophe.After that we consider nonlinear slow sausage surface and slow body waves in magnetic tubes, which are similar to the corresponding counterparts in magnetic slabs. We present a system of two equations describing both types of waves. We briefly discuss the derivation of the Leibovich-Roberts equation for slow sausage surface waves from this system of equations, and present the results of its numerical study. Then we give a brief description of the derivation of the governing equation for slow body waves, which is very similar to its counterpart for slow body waves in magnetic slabs and has very similar properties. We complete this part of the review with presenting the governing equation for non-axisymmetric surface waves in a thin magnetic tube in an incompressible plasma.In the last part of the paper we consider the damping of nonlinear waves in weakly dissipative magnetically structured plasmas. We briefly discuss the application of the obtained results to the problem of heating of the solar corona.KeywordsSurface WaveSolitary WaveSolar PhysMagnetic TubeKink ModeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the ‘rigid lid’ model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.

The propagation of monochromatic nonlinear symmetric hybrid surface waves in a cylindrical nonlinear anisotropic inhomogeneous metal-dielectric waveguide is considered. The physical problem is reduced to solving a transmission eigenvalue problem for a system of ordinary differential equations. Spectral parameters of the problem are propagation constants of the waveguide. The setting is reduced to a new type of nonlinear eigenvalue problem and an analytical method of its solution is developed. The propagation modes are found that have not been previously reported in the literature. For the numerical solution, a method is proposed based on solving an auxiliary Cauchy problem (a version of the shooting method). As a result of comprehensive numerical modeling, new propagation regimes are discovered.

Foreword. I: Theoretical problems concerning propagation of surface wave in elastic anisotropic media. On the role of anisotropy in crystalloacoustics V.I. Alshits. Surface waves of non-Rayleigh type S.V. Kuznetsov. Nonlinearity in elastic surface waves acts nonlocally D.F. Parker. Explicit secular equations for surface waves in an anisotropic elastic half space from Rayleigh to today T.C.T. Ting. II: Bending and edge waves in plates and shells. 'Nongeometrical phenomena' in propagation of elastic surface waves V.M. Babich, A.P. Kiselev. Complex rays and internal diffraction at the cusp edge M. Deschamps, O. Poncelet. Edge waves in the fluid beneath an elastic sheet with linear nonhomogeneity R.V. Goldstein, A.V. Marchenko. On continuum modelling of wave propagation in layered medium: bending waves K.B. Ustinov. Edge-localised bending waves in anisotropic media: energy and dispersion III: Experimental, numerical and semi-analytical methods for analysis of surface waves. Surface electromagnetic perturbations induced by unsteady-state subsurface flow P.M. Adler, V.M. Entov. Resonant waves in a structured elastic halfspace M.V. Ayzenberg-Stepanenko. Mumerical analysis of Rayleigh waves in anisotropic media A.V. Kaptsov. Guided waves in anisotropic media: applications R.A. Kline. A general purpose computer model for calculating elastic waveguide properties, with application to Non-Destructive Testing M.J.S. Lowe, P. Cawley, B.N. Pavlakovic. The influence of the initial stresses on the dynamic instability of an anisotropic cone Y.R. Rossikhin, M.V. Shitikova. Embedding theorem and mutual relation for the interface and shear wavespeeds I.V. Simonov. IV: Applications of surface waves to analysis of fracture and damage. The non-uniqueness of constant velocity crack propagation K.B. Broberg. Embedding formulae for planar cracks R.V. Craster, A.V. Shanin. Wave propagation and crack detection in layered structures E.V. Glushkov, N.V. Glushkova, A.V. Ekhlakov. Author Index.

The nonlinear TE-polarized surface waves localized at the interface between a nonlinear uniform material and a semi-infinite one-dimensional photonic crystal are investigated. We assume that the nonlinear material is right handed and the photonic crystal is made of alternate left-handed metamaterial and right-handed material. We study the intensity-dependent properties of the nonlinear surface waves for both self-focusing and defocusing Kerr-like nonlinearity. Unlike the linear regime, it is shown that in the case of self-focusing nonlinearity the dispersion curve has two branches corresponding to two types of surface mode structures (one structure with a hump at the interface and the other one with two humps). While, in the case of defocusing nonlinearity the dispersion curve has a single branch. We also show that the existence region of the surface waves is intensity dependent (independent) in the case of self-focusing (defocusing) nonlinear regime and the presence of left-handed materials and nonlinear medium provides a possibility for forward or backward waves selection in the given structure by adjusting the intensity parameter at the interface.

In this study, the influence of axial stress on surface wave propagation along cylindrical surfaces is investigated, with particular emphasis on quantifying curvature effects on acoustoelastic coefficients. The classical planar surface wave acoustoelastic formulation is first adopted as a reference. Three-dimensional transient finite element simulations are then performed to model surface wave excitation, propagation, and reception on aluminum cylinders with different radii and excitation frequencies. Stress-free simulations are used to extract surface wave velocities and reference time signals, while prestressed simulations provide stress-induced time delays, from which effective acoustoelastic coefficients are determined. The results indicate that both the surface wave velocity and the acoustoelastic coefficient exhibit clear dependencies on cylinder radius and excitation frequency. Curvature effects are especially pronounced at low frequencies, whereas at higher frequencies the coefficients corresponding to different radii tend to converge. These findings demonstrate that planar surface wave theory may lead to non-negligible errors when applied to cylindrical geometries and provide quantitative guidance for curvature-aware stress evaluation.

The Ostrovsky equation governs the propagation of long nonlinear surface waves in the presence of rotation. It is related to the Korteweg-de Vries (KdV) and the Kadomtsev-Petviashvili models. KdV can be obtained from the equation in question when the rotation parameter γ equals zero. A fundamental solution of the Cauchy problem for the linear Ostrovsky equation is presented in the form of an oscillatory Fourier integral. Another integral representation involving Airy and Bessel functions is derived for it. It is shown that its asymptotic expansion as γ → 0 contains the KdV fundamental solution as the zero term. The Airy transform is used to establish some of its properties. Higher-order asymptotics for γ → 0 on a bounded time interval are obtained for both the fundamental solution and the solution of the linear Cauchy problem for the Ostrovsky equation.

The propagation of surface waves on free and metallized surfaces of cubic and hexagonal crystals is investigated numerically. Surface wave velocity curves and relative differential velocity curves are presented for propagation on typical surfaces of four selected crystals (gallium arsenide, bismuth germanium oxide, zinc oxide, and cadmium sulfide). Special attention is paid to degenerate modes wherein decoupling among the various components of mechanical displacement and the electric field occurs.

Effect of surface scratches on the characteristics of nonlinear Rayleigh surface waves in glass

The impact of subsurface currents induced by internal waves on nonlinear Stokes surface waves is theoretically analyzed. An analytical and numerical solution of the modulation equations are found under the conditions close to the group velocity resonance. It is shown that smoothing of the down current surface waves is accompanied by a relatively high-frequency modulation while the profile of the opposing current is reproduced by the surface wave’s envelope. The possibility of generation of an internal wave forerunner, that is a modulated surface wavepacket, is established. Long surface waves can form the wave modulation forerunner ahead of the internal wave, while the relatively short surface waves create the trace of the internal wave. Modulation of surface waves by the periodic internal wave train may have the characteristic period less than the internal wave period and be no uniform while crossing the current zone. Surface wave excitation by internal waves, observable at their group resonance is efficient only on the opposing current.

The contact of a medium characterized by Kerr nonlinearity and a medium characterized by a stepwise nonlinearity, where the dielectric permittivity depends on the amplitude of the electric field strength, is considered. It is found that an optical domain of finite thickness is formed. Two new types of surface waves are described. The influence of the switching field on the intensity distribution across the interface and on total power flow is analyzed. The intensity at the interface in the case of contact with a nonlinear focusing medium can be maximal, in contrast to the case of contact with a linear medium where the intensity at the interface could not be maximal. The total power flow monotonically decreases with an increase in the nonlinearity parameter and it takes the minimum value at a specific value of the switching amplitude. The largest fraction of the power flow is concentrated on the right side of the optical domain for small values of the switching field starting from a certain value.

It is known [1,2] that an electromagnetic wave can propagate along the planar interface of two linear dielectric media. The strengths of both electric and magnetic field vanish as |x|→ ∞. This is the reason why these waves were called surface waves. It can be shown that such a surface wave exists only if a magnetic field strength vector is parallel to the interface plane, i.e. it is a TM-wave (sometimes it is called a p-polarised wave). If the dielectric permeability of one of the media is a square-law function of electrical field strength, then both propagation of TM wave and the TE wave are possible [3–9]. Such waves were named either non-linear surface waves or non-linear surface polaritons.

Nonlinear surface wave propagation in a plasma slab is investigated using a model in which the perpendicular fluid velocity vanishes at the interface. It is shown that the nonlinear surface waves can propagate as solitons.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The 3-D surface wave Boundary Element Method is applied to the same set of strong motion records as those of Part 1 (Kato et al. , 1993), namely, the long-period strong motion with periods around 8 sec recorded at the JMA (Japan Meteorological Agency) stations in Yokohama and Tokyo during the 1980 Izu-hanto-toho-oki earthquake. This method simulates exact Love and Rayleigh waves in a laterally heterogeneous medium including 3-D basin structures. The needed computer memory and CPU time are made manageable by assuming the inside and outside of the basin to consist of horizontal flat layers. In addition, vertical interfaces are assumed between the basin and the outside bedrock for simplicity in this study. After checking the range of validity of the flat-layer approximation for the Kanto sedimentary basin, the generation and propagation of surface waves in the basin are numerically investigated. In particular, our investigation places special emphasis on the cause of the observed long duration, which could not be explained in Part 1 using the surface wave Gaussian Beam method. When the bedrock outside the western margin of the Kanto basin is incorporated into the model, the observed long duration at the Tokyo station is successfully reproduced. This can be explained by the strong surface waves generated by the surface wave to surface wave conversion at the margin and appearing in Tokyo after the direct surface waves from the epicenter. This result agrees with Kinoshita et al. (1992), who studied records from an array of seismographs in Tokyo. Moreover, when a sedimentary basin of Sagami Bay is included as was done in Part 1, the simulations are greatly improved, particularly at the Yokohama station, which corresponds to the node in the radiation pattern of the source. This is due to the fact that the radiation pattern is strongly affected by the near-source heterogeneity of the Sagami basin. All these results, together with direct comparisons to 2-D modelings, clearly show the strong 3-D effects of the basin structures on the generation and propagation of surface waves for this earthquake.

Surface waves in a nonlinear magnetoelastic conductor of finite electric conductivity