TL;DR: In this paper, a numerical method of second order accuracy is developed to solve acoustic wave equations in heterogeneous media, whose solutions are discontinuous across the interfaces between different wave speeds, using high resolution multi-dimensional flux-limiter methods on a Cartesian grid.

TL;DR: In this article, the theory of scattering for flexural waves is developed for an elastic heterogeneity in a flat thin plate in the context of Mindlin's theory, and some new results are derived for energy flux and contrasted with the equivalent results in Kirchhoff plate theory.

TL;DR: In this article, a flow reversal theorem for sound and acoustic-gravity waves in an arbitrary inhomogeneous moving steady ideal fluid is established, which states symmetry of some wave field quantity with respect to interchange of the source and receiver positions and the simultaneous reversal of the ambient flow.

TL;DR: In this paper, a set of orthogonal and normalized eigenvectors for the 6 × 6 real matrix N(υ) is obtained, and the relationships between the two different classifications and the existence or non-existence of a surface wave in each group are discussed.

TL;DR: In this article, the exact reformulation of the elliptic (two-way) Helmholtz equation in terms of one-way wave equations in a manner which is well-posed for marching is presented.

TL;DR: In this paper, a new exact representation for arbitrary compact source regions using distributions of sources in complex space is presented for both 2D and 3D, and numerical examples are presented for a 3D end-fire array.

TL;DR: The Born-Kirchhoff-Helmholtz (BKH) integral as discussed by the authors is a unified formulation of the Born and Kirchhoff integrals, which can be seen as a natural link between the two formulations.

TL;DR: In this paper, exact expansions for frequency-domain and time-domain fields generated by sources in a finite region of space are presented, where the basis functions are directed monopole or multipole point sources located on a sphere in complex space.

TL;DR: In this paper, the Petviashvili equation was extended to include topographic forcing, and the numerical results showed that topography can alter both the speed and the shape of the monopoles.

TL;DR: The angular spectrum approach to three-dimensional image formation of strong scatterers in scanning acoustic microscopy is developed in this paper, where the image can be represented as a twofold two-dimensional Fourier transform of a far field scattering amplitude of the object.

TL;DR: In this paper, the treatment of artificial boundaries within the framework of characteristic-based finite difference methods for the propagation of elastic waves in large or infinite solids is dealt with, and two different techniques are adopted for the transition layer.

TL;DR: In this paper, the energy velocity of a complex harmonic plane wave in viscous fluids is investigated, where the initial non-conservative energy balance equation is modified into another energy equation, in which the new loss density is, on average, nil.

TL;DR: In this article, the propagation of a transient SH wave in a cylindrically anisotropic solid is considered and an exact solution is obtained as a general solution for an arbitrary cylindrical anisotropy.

TL;DR: In this paper, a vector variant of the BC-method is elaborated for a class of dynamical systems with two different types of waves, which propagate with different velocities interacting with one another.

TL;DR: In this paper, Chotiros et al. modeled ocean sediments as poro-elastic media with relatively high slow-wave speeds and relatively low shear wave speeds and allowed the shear modulus to vanish so that shear waves are ignored.

TL;DR: In this article, a generalized Haskell matrix method is proposed for modeling elastic wave propagation in inhomogeneous media based on mixed variable elastic wave equations and the exponential of matrices, which can be used to accurately simulate all kinds of waves propagating, solving effectively problems of artificial reflection and incident wave excitation.

TL;DR: In this paper, a suitable choice of Sobolev norms for the domain and range spaces of the scattering operator, the restriction to scatterers supported away from caustics is a bounded operator.

TL;DR: In this paper, a unified treatment of stationary points and concavities on the slowness surface of a transversely isotropic elastic material in a zonal plane is given in which some previous results are simplified and their relationship clarified.

TL;DR: In this paper, an exact solution obtained by Green's function method for the linear problem of time-reduced equations governing the forced motion of capillary-gravity waves on water in a circular basin generated by the prescribed horizontal oscillations of its side wall under Hocking's edge conditon was presented.

TL;DR: In this paper, the three-dimensional elastodynamic response of two coplanar penny-shaped cracks embedded in an infinite elastic solid subjected to transient elastic waves is investigated and the effect of the crack distance on the dynamic stress intensity factors is determined.

TL;DR: In this paper, an analytical model for the interaction of a damped solitary wave with a moving external isolated force within a forced dissipative Korteweg-de Vries equation is presented based on a small amplitude for the external force.

TL;DR: In this article, the authors consider the scattering of incident vorticity waves by a rigid rectangular wing in supersonic flow, and complete the solution of the problem using the modified Wiener-Hopf technique.

TL;DR: In this article, the authors derived a variable coefficient multidimensional Burgers equation which models the propagation of a nonlinear sound wave through an incompressible background flow, which is derived from the compressible Euler equations by the combination of a weakly nonlinear acoustics expansion for the sound wave and an incompressive expansion for background flow.

TL;DR: In this article, the problem of radiation and scattering of sound waves caused by the surface vibration of a screened spheriod and by a stationary screened spheroid scattering an incoming plane wave is jointly evaluated.

TL;DR: In this article, the acoustic field in a cylindrical borehole embedded in a horizontally layered infinite medium is studied and the modes in each layer are found to consist of continuous as well as discrete ones, the orthogonality and completeness of which are proven.

TL;DR: In this article, the authors considered linear ageing and non-ageing viscoelastic materials with creep-relaxation kernels containing a weak singularity and showed that the existence of discontinuities of any order is not possible and the solutions behind the wavefront are infinitely smooth.

TL;DR: In this paper, an inhomogeneous medium on the half line with nonconstant potential which is zero beyond depth X is considered and the potential can be reconstructed from the transmitted data provided we have an upper bound on the potential.

TL;DR: In this paper, the authors show that polynomial solitary waves can be hidden in the form of a partial sum of the Fourier series of an intermediate variable (a curvilinear coordinate system), and therefore the balance between instabilities (nonlinear) and dispersive, dissipative, and other effects is well represented in a given nonlinear differential equation.