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Related papers: A k-space method for nonlinear wave propagation

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A new type of wave-mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a…

Pattern Formation and Solitons · Physics 2019-08-06 T. Congy , G. A. El , M. A. Hoefer

We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coefficients, both in the second-order and zero-order terms of…

Numerical Analysis · Mathematics 2025-11-04 Ivan G. Graham , Frances Y. Kuo , Dirk Nuyens , Ian H. Sloan , Euan A. Spence

We analyse the dispersion properties of two types of explicit finite element methods for modelling acoustic and elastic wave propagation on tetrahedral meshes, namely mass-lumped finite element methods and symmetric interior penalty…

Numerical Analysis · Mathematics 2019-01-29 S. Geevers , W. A. Mulder , J. J. W. van der Vegt

We present a wavenumber-explicit convergence analysis of the hp finite element method applied to a class of heterogeneous Helmholtz problems with piecewise analytic coefficients at large wavenumber $k$. Our analysis covers the heterogeneous…

Numerical Analysis · Mathematics 2024-02-05 M. Bernkopf , T. Chaumont-Frelet , J. M. Melenk

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…

Mathematical Physics · Physics 2007-05-23 A. S. Blagovestchenskii , Y. Kurylev , V. Zalipaev

We propose a quantum algorithm that simulates the propagation of a light field through a weakly inhomogeneous medium. The wave equation in the paraxial approximation in inhomogeneous material takes the form of the Schr\"odinger equation…

Quantum Physics · Physics 2026-04-01 Siavash Davani , Martin Gärttner , Falk Eilenberger

We study propagation of stationary waves in disordered non-linear media described by the non-linear Schroedinger equation and show that for given boundary conditions and a given coherent wave incident on a sample the number of solutions of…

Disordered Systems and Neural Networks · Physics 2009-11-10 B. Spivak , A. Zyuzin

The applied method of slowly varying amplitudes of the electrical and magnet vector fields give us the possibility to reduce the nonlinear vector integro-differential wave equation to the amplitude vector nonlinear differential equations.…

Pattern Formation and Solitons · Physics 2007-05-23 Lubomir M. Kovachev

Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a…

Mathematical Physics · Physics 2008-11-25 Xiaoping Xu

We determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel-Korteweg-de Vries-Zakharov-Kuznetsov (SKdVZK) equation which governs…

Plasma Physics · Physics 2022-12-26 S. Phibanchon , M. A. Allen , G. Rowlands

Measurements of seismic wave travel times at the photosphere of the Sun have enabled inferences of its interior structure and dynamics. In interpreting these measurements, the simplifying assumption that waves propagate through a temporally…

Earth and Planetary Astrophysics · Physics 2015-06-16 Shravan Hanasoge , Laurent Gizon , Guillaume Bal

A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…

Fluid Dynamics · Physics 2015-05-26 Roberto Velasco-Segura , Pablo L. Rendón

Stationary scattering of TE and TM waves propagating in an isotropic medium with planar symmetry is described by Bergmann's equation in one dimension. This is a generalization of Helmholtz equation which allows for developing transfer…

Optics · Physics 2025-10-21 Farhang Loran , Ali Mostafazadeh , Cem Yetişmişoğlu

We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of a modulated plane wave. In this regime, the solution exhibits rapid oscillations in both time and space,…

Numerical Analysis · Mathematics 2026-02-05 Yanyan Shi , Christian Lubich

Wave propagation problems are notoriously difficult to solve. Time-harmonic problems are especially challenging in mid and high frequency regimes. The main reason is the oscillatory nature of solutions, meaning that the number of degrees of…

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts the problem reduces to stochastic…

Analysis of PDEs · Mathematics 2023-01-03 Sivaguru S. Sritharan , Saba Mudaliar

In this paper, we investigate propagation phenomena for KPP bulk-surface systems in a cylindrical domain with general section and heterogeneous coefficients. As for the scalar KPP equation, we show that the asymptotic spreading speed of…

Analysis of PDEs · Mathematics 2022-09-01 Beniamin Bogosel , Thomas Giletti , Andrea Tellini

Hawking radiation has become experimentally testable thanks to the many analogue systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion, and give rise to a numerically…

General Relativity and Quantum Cosmology · Physics 2015-06-19 Scott Robertson , Ulf Leonhardt

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of…

Chaotic Dynamics · Physics 2011-07-13 Nicolas Mordant

Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for…

Mathematical Physics · Physics 2011-02-07 Jean-Marc Conoir , Andrew N. Norris