This report concerns the behavior, at large times, of solutions of two-dimensional wave equations in exterior regions. This behavior is related to low frequency calculations for the reduced wave equation. Both Dirichlet and Neumann boundary data are considered, and it is shown that there are differences in the two cases. The results also differ greatly from the corresponding ones in three dimen...

The diffusive-viscous wave equation plays an important role in seismic exploration and it can be used to explain the frequency-dependent reflections observed both in laboratory and field data. The numerical solution to this type of wave equation is needed in practical applications because it is difficult to obtain the analytical solution in complex media. Finite-difference method (FDM) is the m...

For a nonlocally perturbed half-space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined singleand double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green’s function. Due to the unbo...

Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...

This work will explore the discontinuous Galerkin finite element method (DG-FEM) for solving acoustic wave equations in heterogeneous material. High order convergence of DG-FEM will be verified by examples. The numerical error using DG-FEM has the same components as using finite-difference method: grid dispersion and misalignment between numerical grids and material interfaces. Both error compo...

A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are nece...