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We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a…

General Relativity and Quantum Cosmology · Physics 2021-10-19 Thomas Mieling , Piotr T. Chruściel , Stefan Palenta

In the regime of weakly transverse long waves, given long-wave initial data, we prove that the nondimensionalized water wave system in an infinite strip under influence of gravity and surface tension on the upper free interface has a unique…

Analysis of PDEs · Mathematics 2015-05-19 Mei Ming , Ping Zhang , Zhifei Zhang

We present novel analytical solutions for linear-order gravitational waves or tensor perturbations in a flat Friedmann-Robertson-Walker universe containing two perfect fluids, radiation and pressureless dust, and allowing for neutrino…

General Relativity and Quantum Cosmology · Physics 2018-01-01 Andrew J. Wren , Jorge L. Fuentes , Karim A. Malik

This article is concerned with infinite depth gravity water waves in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. Our goal is to study this problem with small wave packet…

Analysis of PDEs · Mathematics 2018-09-14 Mihaela Ifrim , Daniel Tataru

We derive a relativistic field equation for the trace of the metric perturbation beyond the weak field approximation to the Einstein field equations. The dynamics is governed by a massive Klein-Gordon equation on curved space-time, where…

General Physics · Physics 2025-05-02 Victor Atanasov , Avadh Saxena

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space-time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the…

General Relativity and Quantum Cosmology · Physics 2022-03-10 K. E. Osetrin , I. V. Kirnos , E. K. Osetrin , A. E. Filippov

The Gromov-Wasserstein (GW) distance quantifies discrepancy between metric measure spaces and provides a natural framework for aligning heterogeneous datasets. Alas, as exact computation of GW alignment is NP hard, entropic regularization…

Optimization and Control · Mathematics 2024-01-11 Gabriel Rioux , Ziv Goldfeld , Kengo Kato

The Stokes wave problem in a constant vorticity flow is formulated, by virtue of conformal mapping techniques, as a nonlinear pseudodifferential equation, involving the periodic Hilbert transform, which becomes the Babenko equation in the…

Fluid Dynamics · Physics 2019-10-23 Sergey A. Dyachenko , Vera Mikyoung Hur

A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…

Fluid Dynamics · Physics 2017-04-14 Christos Papoutsellis , Gerassimos Athanassoulis

We consider the two-dimensional deep gravity-capillary water waves with point vortices. We first formulate the question in the holomorphic coordinates. Then, we derive an a priori energy estimate for water waves, and show that the water…

Analysis of PDEs · Mathematics 2025-04-28 Lizhe Wan

This paper presents a new numerical model based on the highly nonlinear potential flow theory for simulating the propagation of water waves in variable depth. A new set of equations for estimating the surface vertical velocity is derived…

Fluid Dynamics · Physics 2024-12-02 Jinghua Wang

We show that equations of Newtonian hydrodynamics and gravity describing one-dimensional steady gas flow possess nonlinear periodic solutions. In the case of a zero-pressure gas the solution exhibits hydrodynamic similarity and is…

Astrophysics of Galaxies · Physics 2019-06-26 Eugene B. Kolomeisky

The propagation of electromagnetic waves in a linearly-varying index of refraction is a fundamental problem in wave physics, being relevant in fusion science for describing certain wave-based heating and diagnostic schemes. Here, an exact…

Optics · Physics 2025-04-10 N. A. Lopez

In this article, I present an elementary introduction to the theory of gravitational waves. This article is meant for students who have had an exposure to general relativity, but, results from general relativity used in the main discussion…

Physics Education · Physics 2007-05-23 Indrajit Chakrabarty

We consider the spectra of the 2-dim gravity waves of finite depth linearized at a uniform monotonic shear flow $U(x_2)$, $x_2 \in (-h, 0)$, where the wave numbers $k$ of the horizontal variable $x_1$ is treated as a parameter. Our main…

Analysis of PDEs · Mathematics 2023-06-01 Xiao Liu , Chongchun Zeng

This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. We consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic…

Analysis of PDEs · Mathematics 2016-04-18 Jean-Francois Coulombel , Mark Williams

To obtain the waveform template of gravitational waves (GWs), substantial computational resources and exceedingly high precision are often required. In the previous study [JCAP 11 (2023) 070], we efficiently and accurately calculate GW…

General Relativity and Quantum Cosmology · Physics 2024-07-25 Changkai Chen , Jiliang Jing

The propagation of waves in two space dimensions exhibited by two exact solutions to the field equations of Einstein's unified field theory is investigated under the assumption that the metric s_{ik} is the one already chosen by Kursunoglu…

General Relativity and Quantum Cosmology · Physics 2010-11-11 Salvatore Antoci

The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…

Classical Physics · Physics 2020-02-20 Denys Dutykh

A linear second order wave equation is presented based on cosmological general relativity, which is a space-velocity theory of the expanding Universe. The wave equation is shown to be exactly solvable, based on the Gaussian hypergeometric…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Firmin J. Oliveira