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In rotating stratified flows including in the atmosphere and ocean, inertia-gravity waves (IGWs) often coexist with a geostrophically balanced turbulent flow. Advection and refraction by this flow lead to wave scattering, redistributing IGW…

Fluid Dynamics · Physics 2021-04-21 Miles A. C. Savva , Hossein A. Kafiabad , Jacques Vanneste

This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…

Mathematical Physics · Physics 2015-05-18 Benoit Huard

Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to…

General Relativity and Quantum Cosmology · Physics 2021-08-25 Robert F. Penna

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we…

General Relativity and Quantum Cosmology · Physics 2016-09-05 Takahisa Igata , Shinya Tomizawa

Gravitational-wave (GW) scattering in strong gravitational fields is a central problem in GW lensing. Yet, conventional treatments based on asymptotic expansions suffer from divergences and become unreliable near the optical axis. In this…

General Relativity and Quantum Cosmology · Physics 2026-01-01 Zhao Li , Shaoqi Hou , Wen Zhao

A single spherical antenna is capable of measuring the direction and polarization of a gravitational wave. It is possible to solve the inverse problem using only linear algebra even in the presence of noise. The simplicity of this solution…

General Relativity and Quantum Cosmology · Physics 2009-10-31 S. M. Merkowitz , J. A. Lobo , M. A. Serrano

In this article, we study the inverse scattering problem for the nonlinear fractional Helmholtz equation with cubic nonlinearity in three dimensions, where we recover a compactly supported potential from scattering amplitude.

Analysis of PDEs · Mathematics 2026-03-30 Saumyajit Das , Susovan Pramanik

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Analysis of PDEs · Mathematics 2011-01-24 Tim J. P. M. Op 't Root , Christiaan C. Stolk , Maarten V. de Hoop

This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…

Numerical Analysis · Mathematics 2020-08-13 Gang Bao , Yiwen Lin , Xiang Xu

Mathematically rigorous inversion method is developed to recover compactly supported potentials from the fixed-energy scattering data in three dimensions. Error estimates are given for the solution. An algorithm for inversion of noisy…

Mathematical Physics · Physics 2007-05-23 A. G. Ramm

We consider the scattering of the gravitational waves by the weak gravitational fields of lens objects. We obtain the scattered gravitational waveform by treating the gravitational potential of the lens to first order, i.e. using the Born…

Astrophysics · Physics 2009-11-10 Ryuichi Takahashi , Teruaki Suyama , Shugo Michikoshi

We study an inverse problem for the wave equation, concerned with estimating the wave speed, aka velocity, from data gathered by an array of sources and receivers that emit probing signals and measure the resulting waves. The typical…

Numerical Analysis · Mathematics 2025-08-19 Liliana Borcea , Josselin Garnier , Alexander V. Mamonov , Jörn Zimmerling

We study the statistical properties of an ensemble of weak gravitational waves interacting nonlinearly in a flat space-time. We show that the resonant three-wave interactions are absent and develop a theory for four-wave interactions in a…

General Relativity and Quantum Cosmology · Physics 2017-12-06 S. Galtier , S. V. Nazarenko

A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…

Differential Geometry · Mathematics 2020-01-08 Oliver Lindblad Petersen

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions…

Exactly Solvable and Integrable Systems · Physics 2015-05-20 D. D. Holm , R. I. Ivanov

We consider two formally determined inverse problems for the wave equation in more than one space dimension. Motivated by the fixed angle inverse scattering problem, we show that a compactly supported potential is uniquely determined by the…

Analysis of PDEs · Mathematics 2020-02-19 Rakesh , Mikko Salo

We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…

Mathematical Physics · Physics 2023-07-31 Tadayoshi Adachi , Yuta Tsujii

Gravitons are the quantum counterparts of gravitational waves in low-energy theories of gravity. Using Feynman rules one can compute scattering amplitudes describing the interaction between gravitons and other fields. Here, we consider the…

General Relativity and Quantum Cosmology · Physics 2018-07-18 Nicola Bartolo , Ahmad Hoseinpour , Giorgio Orlando , Sabino Matarrese , Moslem Zarei

We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach…

Analysis of PDEs · Mathematics 2022-01-14 Jeremy G Hoskins , John C Schotland

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…

High Energy Physics - Theory · Physics 2009-10-31 J. M. Maillet , V. Terras