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

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This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

Analysis of PDEs · Mathematics 2025-04-23 Joseph Kraisler , Wei Li , Kui Ren , John C. Schotland , Yimin Zhong

A new rigorous approach for precise and efficient calculation of light propagation along non-uniform waveguides is presented. Resonant states of a uniform waveguide, which satisfy outgoing-wave boundary conditions, form a natural basis for…

Optics · Physics 2017-06-22 S. V. Lobanov , G. Zoriniants , W. Langbein , E. A. Muljarov

This paper provides an alternative methodology for analysis of three-wave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Korteweg-de Vries type of equation with exact…

Fluid Dynamics · Physics 2016-09-06 N. Karjanto

The propagation of nonlinear and dispersive waves in various materials can be described by the well-known Kadomtsev-Petviashvili (KP) equation, which is a (2+1)-dimensional partial differential equation. In this paper, we show that the KP…

Mathematical Physics · Physics 2025-07-21 Harold Berjamin , Michel Destrade , Giuseppe Saccomandi

In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…

Numerical Analysis · Mathematics 2020-03-24 Da Li , Keran Li , Wenyuan Liao

In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…

Analysis of PDEs · Mathematics 2026-01-06 Benjamin Rainer , Barbara Kaltenbacher

Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…

Chaotic Dynamics · Physics 2009-10-29 Pablo Cobelli , Philippe Petitjeans , Agnes Maurel , Vincent Pagneux , Nicolas Mordant

We investigate a nonlinear multiphysics model motivated by ultrasound-enhanced drug delivery. The acoustic pressure field is modeled by Westervelt's quasilinear wave equation to adequately capture the nonlinear effects in ultrasound…

Analysis of PDEs · Mathematics 2024-12-11 Julio Careaga , Vanja Nikolić , Belkacem Said-Houari

Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain.…

Soft Condensed Matter · Physics 2013-05-01 Michel Destrade

In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…

Numerical Analysis · Mathematics 2021-04-07 Eric Chung , Yalchin Efendiev , Sai-Mang Pun , Zecheng Zhang

Starting from first principles, we formulate a theory of wave packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic…

Disordered Systems and Neural Networks · Physics 2011-10-28 Nicolas Cherroret , Thomas Wellens

This paper is devoted to a numerical analysis of a fractional viscoelastic wave propagation model that generalizes the fractional Maxwell model and the fractional Zener model. First, we convert the model problem into a velocity type…

Numerical Analysis · Mathematics 2025-07-17 Hao Yuan , Xiaoping Xie

We investigate models for nonlinear ultrasound propagation in soft biological tissue based on the one that serves as the core for the software package k-Wave. The systems are solved for the acoustic particle velocity, mass density, and…

Analysis of PDEs · Mathematics 2024-06-03 Ben Cox , Barbara Kaltenbacher , Vanja Nikolić , Felix Lucka

We consider semilinear hyperbolic systems with a trilinear nonlinearity. Both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, and typical solutions oscillate with frequency proportional…

Analysis of PDEs · Mathematics 2022-07-01 Julian Baumstark , Tobias Jahnke

We investigate the transmission of scalar, electromagnetic, and linearized odd-parity gravitational waves in a static spacetime characterized by a spherical distribution of matter in the form of thin concentric equidistant shells of equal…

General Relativity and Quantum Cosmology · Physics 2024-07-04 Rubén O. Acuña-Cárdenas , Olivier Sarbach , Luca Tessieri

In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…

Numerical Analysis · Mathematics 2022-10-21 Yifan Chen , Thomas Y. Hou , Yixuan Wang

A time-domain approach is proposed for the propagation of ultrashort electro- magnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the…

Optics · Physics 2007-05-23 Charles Varin , Michel Piché

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…

Numerical Analysis · Mathematics 2022-12-21 R. Sancho , V. Rey de Pedraza , P. Lafourcade , R. A. Lebensohn , J. Segurado

This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…

Classical Physics · Physics 2018-12-05 John Hollkamp , Mihir Sen , Fabio Semperlotti

We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…

General Physics · Physics 2013-09-17 S. Habib Mazharimousavi , Ashkan Roozbeh , M. Halilsoy