Related papers: A k-space method for nonlinear wave propagation
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…
A group of high order Gautschi-type exponential wave integrators (EWIs) Fourier pseudospectral method are proposed and analyzed for solving the nonlinear Klein-Gordon equation (KGE) in the nonrelativistic limit regime, where a parameter…
Accurate simulation of nonlinear acoustic waves is essential for the continued development of a wide range of (high-intensity) focused ultrasound applications. This article explores mixed finite element formulations of classical strongly…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane wave component (plane wave limit), separately. For gain media, we…
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this…
We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…
The propagation of a quasi-harmonic electromagnetic wave in a bulk hyperbolic dielectric metamaterial is considered. If the group velocities dispersion is not taken into account, then wave propagation can be described either by the…
In this paper the theory and simulation results are presented for 3D vector cylindrical rotationally symmetric electromagnetic wave propagation in an isotropic nonlinear medium using a modified finite-difference time-domain general vector…
The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…
This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution- free also in the case…
A time-domain numerical code based on the constitutive relations of nonlinear acoustics for simulating ultrasound propagation is presented. To model frequency power law attenuation, such as observed in biological media, multiple relaxation…
Simple yet accurate results for radiative transfer in layered media with discontinuous refractive index are obtained by the method of K-integrals, originally developed for neutron transport analysis. These are certain weighted integrals…
In this paper, we prove the existence of the spreading speed of nonlocal KPP equations in two cases: 1. The media is almost periodic and the kernel of diffusion is continuous; 2. The media is periodic and the diffusion is not continuous but…
We consider an inverse problem for a Westervelt type nonlinear wave equation with fractional damping. This equation arises in nonlinear acoustic imaging, and we show the forward problem is locally well-posed. We prove that the smooth…
In this paper we study the effect of rotation on nonlinear wave phenomena in weakly dispersive media modeled by the Korteweg-de Vries equation on the real line. It is well known that smoothing in the case of the KdV equation with periodic…
This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel-faces. This approach introduces the time-averaged Poynting vector modulus as field…