English
Related papers

Related papers: Integral and asymptotic properties of solitary wav…

200 papers

Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…

Fluid Dynamics · Physics 2023-11-01 Didier Clamond , Joris Labarbe

Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…

Fluid Dynamics · Physics 2025-11-21 Alan Riquier , Emmanuel Dormy

In this article we consider irrotational gravity water waves with finite bottom. Our goal is two-fold. First, we represent the equations in holomorphic coordinates and discuss the local well-posedness of the problem in this context. Second,…

Analysis of PDEs · Mathematics 2016-07-12 Benjamin Harrop-Griffiths , Mihaela Ifrim , Daniel Tataru

A detailed investigation is presented of a simple unidirectional finite-energy solution of the 3D wave equation. Its asymptotics as a spatial point runs to infinity with the wave propagations speed is a standard spherical wave as z < 0,…

Optics · Physics 2025-09-10 Alexandr B. Plachenov , Aleksei P. Kiselev

This paper investigates solitary water waves propagating along the surface of a two-dimensional dielectric fluid with constant vorticity in the presence of an external electric field. We formulate the system as a nonlinear free boundary…

Analysis of PDEs · Mathematics 2026-04-28 Tingting Feng , Yong Zhang , Zhitao Zhang

We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a…

Analysis of PDEs · Mathematics 2024-08-27 Anna-Mariya Otsetova , Erik Wahlén , Jörg Weber

This paper is concerned with two-dimensional, steady, periodic water waves propagating at the free surface of water either in a flow of finite depth and constant vorticity over an impermeable flat bed or in an irrotational flow of great…

Analysis of PDEs · Mathematics 2014-04-25 Peter de Boeck

We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation…

Analysis of PDEs · Mathematics 2024-08-27 Erik Wahlén , Jörg Weber

We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom…

Analysis of PDEs · Mathematics 2026-02-20 Martino Prizzi

We investigate when plane-wave memory admits standard outgoing free data beyond the idealized sandwich-wave approximation. For a Brinkmann plane wave with profile $A(U)$, the commonly used condition $A(U)|_{U\to\infty}=0$ is not sufficient…

General Relativity and Quantum Cosmology · Physics 2026-05-29 Qi-Liang Zhao , Li-Ming Cao

Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…

Pattern Formation and Solitons · Physics 2008-01-04 Gideon Simpson , Michael I. Weinstein

We examine current numerical relativity computations of gravitational waves, which typically determine the asymptotic waves at infinity by extrapolation from finite (small) radii. Using simulations of a black hole binary with accurate wave…

General Relativity and Quantum Cosmology · Physics 2009-12-31 Denis Pollney , Christian Reisswig , Nils Dorband , Erik Schnetter , Peter Diener

We consider the capillary-gravity water-waves problem of finite depth with a flat bottom of one or two horizontal dimensions. We derive the modulation equations of leading and next-to-leading order in the hyperbolic scaling for three weakly…

Analysis of PDEs · Mathematics 2016-02-02 Ioannis Giannoulis

This paper deals with the dead-water phenomenon, which occurs when a ship sails in a stratified fluid, and experiences an important drag due to waves below the surface. More generally, we study the generation of internal waves by a…

Analysis of PDEs · Mathematics 2021-11-18 Vincent Duchene

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume…

Analysis of PDEs · Mathematics 2021-11-18 Vincent Duchene

Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions…

Classical Physics · Physics 2018-02-07 Didier Clamond

We investigate steady symmetric gravity water waves on finite depth. For non-positive vorticity it is shown that the particles display a mean forward drift, and for a class of waves we prove that the size of this drift is strictly…

Mathematical Physics · Physics 2007-12-05 Mats Ehrnstrom

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…

Mathematical Physics · Physics 2011-06-21 Delia Ionescu-Kruse

The motion of an interface separating two fluids under the effect of electric fields is a subject that has picked the attention of researchers from different areas. While there is an abundance of studies investigating the free surface wave…

Fluid Dynamics · Physics 2023-03-29 Marcelo V. Flamarion , Tao Gao , Roberto Ribeiro-Jr

The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of…

Fluid Dynamics · Physics 2022-11-28 Evgeny A. Kochurin , Olga V. Zubareva , Nikolay M. Zubarev