In this paper, we present a numerical scheme for the propagation of acoustic waves in a heterogeneous medium in the context of the finite volume evolution Galerkin (FVEG) method (M. Lukáčová-Medvid’ová et al. J. Comput. Phys., 183:533–562, 2002). As a mathematical model we consider a wave equation system with space dependent wave-speed and impedance, which is used to study the wave propagation ...

V 2 A + C 2 s + V ∆t/∆x < 1 is satisfied, where VA is the Alfvén wave speed, Cs is the sound wave speed, and V is the flow speed. Unconditional stability for sound and Alfvén waves with arbitrary time step ∆t is achieved by adding a semi-implicit term to the momentum equation. However, the flow CFL condition V∆t/∆x <must still be satisfied. The resistivity and viscosity are advanced implicitly ...

optical interferometry is being used as an efficient tool to analyse smooth surfaces for more than a century. although, due to introduction of novel computer assisted analyzing techniques and array detectors, like ccd, the speed and the precision of processing have been increased tremendously, but the main equation involved is not changed. the main equation is the intensity distribution in the ...

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently ...

S U M M A R Y Sensitivity kernels for fundamental mode surface waves at finite frequency for 2-D phase speed and 3-D shear wave speed are constructed based on the Born and Rytov approximations working with a potential representation for surface waves. The use of asymptotic Green’s functions for scalar wave equations provides an efficient way to calculate the Born or Rytov kernels. The 2-D sensi...

In this paper we study the existence and qualitative properties of travelling waves associated to a nonlinear flux limited partial differential equation coupled to a Fisher–Kolmogorov–Petrovskii–Piskunov type reaction term. We prove the existence and uniqueness of finite speed moving fronts of C classical regularity, but also the existence of discontinuous entropy travelling wave solutions.

We study here instability problems of standing waves for the nonlinear Klein-Gordon equations and solitary waves for the generalized Boussinesq equations. It is shown that those special wave solutions may be strongly unstable by blowup in finite time, depending on the range of the wave’s frequency or the wave’s speed of propagation and on the nonlinearity.

The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigate...