Wave Motion最新文献

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.

We investigate counterpropagating optical solitary waves – nematicons – in non-homogeneously oriented nematic liquid crystals. A non-symmetric angular distribution of the optic axis versus beam propagation provides the solitons with direction-dependent trajectories. By performing numerical experiments in realistic planar samples, we launch nematicons in opposite directions and examine the resulting non-specular transmission in terms of optical nonreciprocity and isolation.

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of local effects, both on the (small) scale of the wavelength, are observed: one within one wavelength of the boundaries of the slab, and one inside the domain (at a distance from the boundaries large compared to the wavelength). The former impacts the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

This article examines the soliton-type solutions, their interactions, and the integrable properties of a non-autonomous perturbed Gardner KP (NPGKP) equation. For the NPGKP equation under consideration, a bilinear structure, and a Bäcklund transformation are designed explicitly, which claim the integrability of the system under some constraints. The stability of the obtained solutions is discussed using modulation instability. The bilinear form demonstrates the dynamic characteristics of multiple solitons, breathers, and their interactions in response to external impulses. Furthermore, it allows for determining the solitons’ amplitudes and velocities. The two-soliton solution yields a first-order breather solution. At the same time, the analytical investigation focuses on the interaction between a single breather and a single-soliton within the multi-soliton solution. This investigation also identifies the resonance of $Y$-shaped solitons and examines the dynamical characteristics of the interaction between resonant $Y$-shaped solitons and $M$-fissionable pulses. The multi-shock solutions and the collisions between shocks are analyzed in the presence of external influences. Graphical representations of the relationships between different sorts of achieved solutions are provided explicitly.

This study presents a mathematical model of transmission loss (TL) for finite-sized corrugated-core sandwich panels subjected to aerodynamic pressure. The aerodynamic pressure is calculated using a cross-power spectral density function. The propagation of sound waves within a corrugated sandwich-panel structure is described using the wave propagation method. The corrugated-stiffened panel is equivalently represented using translational and rotational springs. Fluid‒structure coupling is considered by enforcing interface velocity continuity conditions at the fluid‒solid interface. A modal superposition method is used to establish the dynamic equations of the corrugated-core sandwich panel. The velocity response, radiated power, and TL of the corrugated-core sandwich panel are obtained by solving dynamic equations. A mathematical model is employed to investigate the acoustic characteristics of corrugated-core sandwich panels. Subsequently, the distinctions in the TL of a corrugated sandwich panel under acoustic and aerodynamic pressures (turbulence) are discussed. The influences of the flow velocity, corrugated-core sandwich-panel thickness, and corrugated-stiffener angle on the TL performance of the panel are investigated. This analysis contributes to a deeper understanding of the acoustic design of corrugated-core sandwich panels.

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward scattering problem may be readily analyzed, the inverse problem is very challenging as it is ill-posed, high-dimensional, and known to admit non-unique solutions. Therefore, the inverse design of multiple scattering fields and remote sensing of scattering elements remains a topic of great interest. Motivated by recent advances in physics-informed machine learning, we develop a deep neural network that is capable of predicting the locations of scatterers by evaluating the patterns of a target wavefield. We present a modeling and training formulation to optimize the multi-functional nature of our network in the context of inverse design, remote sensing, and wavefield engineering. Namely, we develop a multi-stage training routine with customized physics-based loss functions to optimize models to detect the locations of scatterers and predict cluster configurations that are physically consistent with the target wavefield. We demonstrate the efficacy of our model as a remote sensing and inverse design tool for three scattering problem types, and we subsequently apply our model to design clusters that direct waves along preferred paths or localize wave energy. Hence, we present an effective model for multiple scattering inverse design which may have diverse applications such as wavefield imaging or passive wave energy control.