Wave Motion最新文献

In this paper, we study the propagation of Shear Horizontal (SH) waves in the interfaces of a piezoelectric/piezomagnetic/piezoelectric (PiezoE/ PiezoM/ PiezoE) structure with a magnetical, imperfect magnetic, electric, and mechanical condition at interfaces. The inclusion of magnetical imperfections produced several new results, such as a general dispersion relation and expressions for some limit cases, which were not reported previously in the literature, predicting the existence of interfacial waves. Employing numerical calculations, dispersion curves for this kind of structure are presented for the first time. It can be shown that the magnetical imperfection interface influences the dispersion curves. Our results show that especially magnetic imperfections have a significant influence on the dispersion curves.

In this manuscript we investigate the Benjamin–Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave interactions in deep water without restrictions on spectral bandwidth. Spatial evolution, with measurements at discrete locations, is pertinent for laboratory hydrodynamic experiments, such as in wave flumes, which rely on time-series measurements at fixed gauges installed along the facility. This setting is likewise appropriate for experiments in electromagnetic and plasma waves. Through a reformulation of the problem for a degenerate quartet, we bring to bear techniques of phase-plane analysis which elucidate the full dynamics without recourse to linear stability analysis. In particular we find hitherto unexplored breather solutions and discuss the optimal transfer of energy from carrier to sidebands. We show that the maximal energy transfer consistently occurs for smaller side-band separation than the fastest linear growth rate. Finally, we discuss the observability of such discrete solutions in light of numerical simulations.

This review provides a detailed discussion of both the mathematical treatment and the impact of a frequency-dependent Kerr nonlinearity on the propagation of short pulses in optical fibers. We revisit the theoretical framework required to deal with the frequency dependence of the nonlinear response without incurring any physical inconsistencies, such as the non-conservation of the photon number. Then, we point out the role of the zero-nonlinearity wavelength, its interplay with the zero-dispersion wavelength, and their influence on evolution of optical pulses in optical fibers, specifically by looking at soliton propagation and the ensuing generation of Cherenkov radiation. Finally, by means of a space–time analogy involving the collision of a weak control pulse and an intense soliton, we describe an all-optical switching scheme in the presence of a zero-nonlinearity wavelength within a photon-conserving framework.

Using a specific Darboux transformation, we construct solutions to the functional difference KdV equation in terms of Casorati determinants. We give a complete description of the method and the corresponding proofs. We construct explicitly some solutions for the first orders.

This paper concentrates on a (3+1)-dimensional nonlinear evolution equation. By introducing a transformation, the (3+1)-dimensional nonlinear evolution equation is decomposed into three integrable (1+1)-dimensional models. On the basis of a quartet Lax pair, we build the associated matrix Riemann–Hilbert problem. As a consequence, solving the obtained matrix Riemann–Hilbert problem with the identity jump matrix, corresponding to the reflectionless, the soliton solution to the (3+1)-dimensional nonlinear evolution equation is acquired. Specially, the one-soliton solutions are worked out and analyzed graphically.

In this paper, state transition waves are investigated in a (2+1)-dimensional Korteweg–de Vries-Sawada-Kotera-Ramani equation by analyzing characteristic lines. Firstly, the $N$-soliton solutions are given by using the Hirota bilinear method. The breather and lump waves are constructed by applying complex conjugation limits and the long-wave limit method to the parameters. In addition, the transition condition of breather and lump wave are obtained by using characteristic line analysis. The state transition waves consist of quasi-anti-dark soliton, M-shaped soliton, oscillation M-shaped soliton, multi-peak soliton, W-shaped soliton, and quasi-periodic wave soliton. Through analysis, when solitary wave and periodic wave components undergo nonlinear superposition, it leads to the formation of breather waves and transformed wave structures. It can be used to explain the deformable collisions of transformation waves after collision. Furthermore, the time-varying property of transformed waves are studied using characteristic line analysis. Based on the high-order breather solutions, the interactions involving breathers, state transition waves, and solitons are exhibited. Finally, the dynamics of these hybrid solutions are analyzed through symbolic computations and graphical representations.

We study the problem of a transferring electron along a lattice of phonons, in the continuous long wave limit, holding periodic on-site and linear longitudinal interactions in Holstein’s approach. We thus find that the continuum limit of our modeling produces an effective coupling between the linear Schrödinger and sine–Gordon equations. Then, we take advantage of the existence of trapped kink–anti kink solutions in the sine–Gordon equation to variationally describe traveling localized coupled solutions. We validate our variational findings by solving numerically the full coupled system. Very reasonable agreement is found between the variational and full numerical solutions for the amplitude evolution of both profiles; the wave function and the trapped kink–anti kink. Our results show the significance of permitting longitudinal interactions in the Holstein’s approach to hold trapped localized solutions. It is actually found a critical ratio between longitudinal and on-site interactions, as depending on the velocity of propagation, from where coupled localized solutions exist.

Waves in space-dependent and in time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement of time- and space-coordinates), the solutions are dissimilar.

We present a systematic treatment of wave propagation and scattering in 1D space-dependent and in 1D time-dependent materials. After formulating unified equations, we discuss Green’s functions and simple wave field representations for both types of material. Next we discuss propagation invariants, i.e., quantities that are independent of the space coordinate in a space-dependent material (such as the net power-flux density) or of the time coordinate in a time-dependent material (such as the net field-momentum density). A discussion of general reciprocity theorems leads to the well-known source-receiver reciprocity relation for the Green’s function of a space-dependent material and a new source-receiver reciprocity relation for the Green’s function of a time-dependent material. A discussion of general wave field representations leads to the well-known expression for Green’s function retrieval from the correlation of passive measurements in a space-dependent material and a new expression for Green’s function retrieval in a time-dependent material.

After an introduction of a matrix–vector wave equation, we discuss propagator matrices for both types of material. Since the initial condition for a propagator matrix in a time-dependent material follows from the boundary condition for a propagator matrix in a space-dependent material by interchanging the time- and space-coordinates, the propagator matrices for both types of material are interrelated in the same way. This also applies to representations and reciprocity theorems involving propagator matrices, and to Marchenko-type focusing functions.

Non-reflective wave propagation is of great importance for applications because it allows energy to be transmitted over long distances. The paper discusses the method of reducing the equations of the linear theory of shallow water to a wave equation with a variable coefficient in the form of an inverse hyperbolic sine, the solution of which is represented as a composition of traveling waves. Thanks to this, a new non-reflective bottom profile has been obtained, which reaches a constant at infinity. Wave behavior on the shore is discussed, as well as the conditions under which the wave field remains finite on it. A detailed analysis of the obtained exact solution to the shallow water equations is given in the paper.

The exploration of rational solutions of first and second orders, along with the investigation of modulation instability, has been conducted in the left-handed coplanar waveguide based on split-ring resonators. This study is inspired by the research of Abbagari et al. (0000), where solitonic rogue wave structures were derived as manifestations of the growth rate of modulation instability. Under this argument, we have used the perturbations method to derive the Kundu–Eckhaus equation to analyze the characteristics of the high-order rogue waves. Beside these findings, we have realized that rogue wave structures are propagated in the left-handed frequency bands. We also notice that modulation instability growth develops in the frequency bands when the product of the nonlinearity coefficient and dispersion coefficient is positive. Through a numerical simulation, we have developed the rogue wave objects to confirm our analytical predictions. Another significant aspect addressed in this study is the sensitivity of both modulation instability and higher-order rogue waves to the normalized parameter introduced through the third-order expansion of the voltage-dependent capacitance and perturbed wave number. The long-lived results have been equally validated for specific times of propagation. These results could be used in the future in left-handed metamaterials for several applications.