We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian
A technique for obtaining refined heuristic solutions for problems with electromagnetic wave diffraction by scatterers with non-ideal boundary conditions is proposed. Based on the method of fundamental components for the problem of TE-polarized wave...
In this paper, we obtain dispersion relations corresponding to plane wave solutions in Lorentz-breaking extensions of gravity with dimension 3, 4, 5 and 6 operators. We demonstrate that these dispersion relations display a usual Lorentz-invariant mod...
The scattering of elastic waves by underground cavities is an active research topic for its broad applications in various fields, such as earthquake engineering, the blast resistance of underground structures, geophysical exploration, etc. In most pr...
The tuned mass damper (TMD) is widely used for vibration mitigation, especially in high-rise buildings where significant soil-structure interaction (SSI) effects are usually involved. This creates a need to consider SSI effects in TMD design. In this...
A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with the wave and whether gravitational energy transfer is null. It is found that this Bel-Robinson e...
I present an exact and explicit solution to the nonlinear governing equations in the equatorial f-plane, describing geophysical edge waves propagating over a plane-sloping beach, in the presence of underlying uniform currents. I also derive the analy...
We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the...
In this article, we present a methodological and systematic approach to solving the Klein–Gordon–Fock equation using the separation of variables method, with particular emphasis on its formulation in light-front coordinates. Although the...
The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann...
This paper addresses the problem of interactive auralization of enclosures based on a finite superposition of plane waves. For this, room acoustic simulations are performed using the Finite Element (FE) method. From the FE solution, a virtual microph...
Ultrasound plane wave imaging technology has been applied to more clinical situations than ever before because of its rapid imaging speed and stable imaging quality. Most transducers used in plane wave imaging are linear arrays, but their structures...
We consider the propagation of electromagnetic waves in the Friedmann–Lemaître–Robertson–Walker metric. The exact solutions for plane and spherical wave are written down. The corresponding redshift, amplitude change, and dispe...
A solution for the two-dimensional scattering and diffraction of plane SH waves by fixed-rigid cylinder of arbitrary shape in an elastic infinite medium is presented. The wave field for arbitary geometry in this paper is computed numericaly by the me...
The motion of a circular elastic plate floating on the surface is investigated in the time-domain. The solution is found from the single frequency solutions, and the method to solve for the circular plate is given using the eigenfunction matching met...
A boundary integral equations method (BIEM) for a graded magneto-electro-elastic (MEE) half-plane with cracks under an incident time-harmonic SH wave is presented. The method is based on an analytically derived Green’s function and a free-field...
A plane wave reconstruction technique is presented for the solution of Helmholtz’s equation governing wave propagation in equilateral triangular electromagnetic waveguides in order to aid in the classification of symmetric and antisymmetric modes as...
We present first principle calculations on formation and binding energies for Cu and Zn as solute atoms forming small clusters up to nine atoms in Al-Cu and Al-Zn alloys. We employ a density-functional approach implemented using projector-augmented w...
In previous work, we considered a four-quadrant Riemann problem for a
Fractal geometries consistently provide solutions to several electromagnetic design problems. In this paper, fractal geometries such as Hilbert and Moore curves are used to design efficient High-Impedance Surfaces. Modern communication devices have m...
A review of simple solutions to the linear wave equation in three spatial variables, involving arbitrary functions, is given. Physicists’ interest in these solutions is primarily motivated by the need for a convenient description of spatiotempo...
The diffraction of plane electromagnetic waves by an open parallel plate waveguide with dielectric loading is investigated rigorously by using the Fourier transform technique. This method of formulation gives rise to Wiener- Hopf equations. The solut...
The propagation of optical soliton profiles in plasma physics and atomic structures is represented by the
The focus of this work is to determine at which threshold can the results for both plane and spherical wave incidence assumptions either converge or deviate when performing multiple diffraction attenuation calculations. The analysis has been carried...
Accurate and efficient numerical wave generation and absorption of two-dimensional nonlinear periodic waves traveling on a steady, uniform current were carried out in a potential, fully nonlinear numerical wave tank. The solver is based on the Β...
Electromagnetic fields in bulk bianisotropic media contain plane waves whose k-vectors can be found using the method of the index of refraction’s operator and belong to the Fresnel wave surfaces that fall into one of the five hyperbolic classes...
In this article, the general solution of the tachyonic Klein–Gordon equation is obtained as a Fourier integral performed on a suitable path in the complex
Precise stochastic approaches to quantitatively calculate the source uncertainties offers the opportunity to eliminate the influence of anisotropy on moment tensor inversion. The effects of ignoring anisotropy were tested by using homogeneous Green&r...
The existence of local terrain has a great influence on the scattering and diffraction of seismic waves. The wave function expansion method is a commonly used method for studying terrain effects, because it can reveal the physical process of wave sca...
It has long been known that plane wave solutions of the cubic nonlinear Schrödinger Equation (NLS) are linearly unstable. This fact is widely known as modulation instability (MI), and sometimes referred to as Benjamin–Feir instability in t...
This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel (
This work explores the qualitative dynamics of the modified unstable time-fractional nonlinear Schrödinger equation (mUNLSE), a model applicable to nonlinear wave propagation in plasma and optical fiber media. By transforming the governing equat...
Seismic waves propagation with an oblique angle to the tunnel axis will cause asynchronous tunnel motions and have a significant effect on the axial response. A high-precision 2.5D finite element method is established in the frequency domain to simul...
Based on the image method and addition theorem of spherical vector wave functions, an analytical solution of the multiple scattering by a buried medium-coated conducting sphere is proposed in this paper. An iterative process to obtain the scattered e...
This paper presents a mathematical model that describes the propagation of internal inertia–gravity waves in a stratified atmosphere under the approximations of an incompressible fluid and a traditional β-plane. It demonstrates that, in th...
We critically reexamine traveling-wave solutions and Benjamin–Feir instability for a Schrödinger–Hirota equation with power-law nonlinearity. A traveling-wave reduction, Hamiltonian phase-plane analysis, direct substitution, and symb...
The asymptotic approach is suggested for the description of interacting surface and internal oceanic solitary waves. This approach allows one to describe stationary moving symmetric wave patterns consisting of two plane solitary waves of equal amplit...
A major problem that often arises in modeling Micro Electro Mechanical Systems (MEMS) such as Surface Acoustic Wave (SAW) sensors using Finite Element Analysis (FEA) is the extensive computational capacity required. In this study a new approach is ad...
Most existing depth-averaged granular flow theories assume that dry, cohesionless granular materials are incompressible, with the void ratio among grains remaining spatially and temporally invariant. However, recent large-scale experiments showed tha...
We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which...
This paper derives an analytical model of a straight beam with a T-shaped cross section for use in the high-frequency range, defined here as approximately 1 to 35 kHz. The web, the right part of the flange, and the left part of the flange of the T-be...
The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as...
The solution to an ill-posed linear inverse problem requires the use of regularization methods to achieve a stable approximation solution. One powerful approach is the truncated singular value decomposition (TSVD), but it requires an appropriate choi...
This study examines the Chen–Lee–Liu dynamical equation, which represents the propagation of optical pulses in optical fibers and plasma. A new extended direct algebraic technique and Nucci’s scheme are used to find new solitary wav...
We revisit a hyperbolic wildfire model based on reaction–diffusion dynamics with relaxation effects and extend it by incorporating an advection transport term that accounts for wind-driven fire spread. After a planar two-dimensional reformulati...
Electromagnetic (EM) wave propagation inside and along the surface of the human body is the subject of active research in the field of biomedical applications of microwaves. This research area is the basis for wireless monitoring of biological object...
In physics, mathematics, and other disciplines, new integrable equations have been found using the P-test. Novel insights and discoveries in several domains have resulted from this. Whether a solution is oscillatory, decaying, or expanding exponentia...
A system of initially immobile spherical liquid drops placed in another liquid in the field of a propagating acoustic wave is considered. The acoustic radiation force acting on each spherical liquid drop is determined as the function of the incident...
An analytical solution is presented for scattering nonplanar SH waves emanating from a fault source using a lined tunnel. The lined tunnel is assumed to be an annular elastic solid in half-space. A simplified circular arc fault model is employed to r...
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