Related papers: Explicit secular equation for Scholte waves over a…
Rayleigh waves are considered for crystals possessing at least one plane of symmetry. The secular equation is established explicitly for surface waves propagating in any direction of the plane of symmetry, using two different methods. This…
The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane…
The propagation of surface acoustic waves in a rotating anisotropic crystal is studied. The crystal is monoclinic and cut along a plane containing the normal to the symmetry plane; this normal is also the axis of rotation. The secular…
Attention is given to surface waves of shear-horizontal modes in piezoelectric crystals permitting the decoupling between an elastic in-plane Rayleigh wave and a piezoacoustic anti-plane Bleustein-Gulyaev wave. Specifically, the crystals…
The goal of this work is to determine whole classes of solitary wave solutions general for wave equations.
Scattering of a scalar particle on a crystalline plane with quadratic cell and identical fixed scatterers is solved precisely. Contradiction of the standard scattering theory is pointed out.
The propagation of surface (Rayleigh) waves over a rotating orthorhombic crystal is studied. The crystal possesses three crystallographic axes, normal to the symmetry planes: the half-space is cut along a plane normal to one of these axes,…
The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if…
The study of elastic surface waves under impedance boundary conditions has become an intensive field of research due to their potential to model a wide range of problems. However, even when the secular equation, which provides the speed of…
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our formula leads to a stable and high-order numerical scheme that…
Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of…
This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic liquid crystals. By using the method of characteristics, we…
Seafloor topography can excite strong interface waves called Scholte waves that are often dispersive and characterized by slow propagation but large amplitude. This type of wave can be used to invert for near seafloor shear wave velocity…
The quantum-mechanical expression for the polarization of a crystalline solid does not bear any resemblance to the (trivial) expression for the dipole of a bounded crystallite; and in fact it has been proved via a conceptually different…
Conditions on the elastic stiffnesses of anisotropic crystals are derived such that circularly polarized longitudinal inhomogeneous plane waves with an isotropic slowness bivector may propagate for any given direction of the normal to the…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…