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The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering…

Exactly Solvable and Integrable Systems · Physics 2024-04-05 Peng-Fei Han , Ru-Suo Ye , Yi Zhang

Using uniform global Carleman estimates for discrete elliptic and semi-discrete hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation,…

Analysis of PDEs · Mathematics 2014-09-29 Lucie Baudouin , Sylvain Ervedoza , Axel Osses

Starting from the magnetic total-moment sum rule of neutron scattering, we derive an explicit connection between ordered-moment reduction and the long-time limit of the intermediate scattering function. We show that this time-domain…

Strongly Correlated Electrons · Physics 2026-03-04 Fanjun Xu

A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…

Atomic Physics · Physics 2023-08-23 V. A. Gradusov , S. L. Yakovlev

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…

Analysis of PDEs · Mathematics 2018-05-21 Samuel Cogar , David Colton , Peter Monk

We consider a half-order time-fractional diffusion equation in an arbitrary dimension and investigate inverse problems of determining the source term or the diffusion coefficient from spatial data at an arbitrarily fixed time under some…

Analysis of PDEs · Mathematics 2020-10-21 X. Huang , A. Kawamoto

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is…

Numerical Analysis · Mathematics 2024-12-20 Thanh T. Nguyen , Michael V. Klibanov

Compton scattering of polarized radiation in a strong magnetic field is considered. The recipe for calculation of the scattering matrix elements, the differential and total cross sections based on quantum electrodynamic (QED) second order…

High Energy Astrophysical Phenomena · Physics 2016-05-11 Alexander A. Mushtukov , Dmitrij I. Nagirner , Juri Poutanen

We continue the study of the theory of scattering for some long range Hartree equations with potential |x|^-gamma, performed in a previous paper, denoted as I, in the range 1/2 < gamma < 1. Here we extend the results to the range 1/3 <…

Analysis of PDEs · Mathematics 2015-06-15 J. Ginibre , G. Velo

In this paper we consider an inverse problem for the $n$-dimensional random Schr\"{o}dinger equation $(\Delta-q+k^2)u = 0$. We study the scattering of plane waves in the presence of a potential $q$ which is assumed to be a Gaussian random…

Analysis of PDEs · Mathematics 2016-07-13 Pedro Caro , Tapio Helin , Matti Lassas

We establish Lipschitz stability for both the potential and the initial conditions from a single boundary measurement in the context of a hyperbolic boundary initial value problem. In our setting, the initial conditions are allowed to…

Analysis of PDEs · Mathematics 2025-11-25 Shiqi Ma

The Schroedinger equation on the half line is considered with a real-valued, integrable potential having a finite first moment. It is shown that the potential and the boundary conditions are uniquely determined by the data containing the…

Mathematical Physics · Physics 2009-11-10 Tuncay Aktosun , Ricardo Weder

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…

Analysis of PDEs · Mathematics 2009-12-16 Xiaodong Liu , Bo Zhang

In this paper, we adapt the well-known \emph{local} uniqueness results of Borg-Marchenko type in the inverse problems for one dimensional Schr{\"o}dinger equation to prove \emph{local} uniqueness results in the setting of inverse…

Mathematical Physics · Physics 2015-01-16 Thierry Daude , Damien Gobin , François Nicoleau

Let $A(\beta,\alpha,k)$ be the scattering amplitude corresponding to a real-valued potential which vanishes outside of a bounded domain $D\subset \R^3$. The unit vector $\alpha$ is the direction of the incident plane wave, the unit vector…

Mathematical Physics · Physics 2009-06-21 A. G. Ramm

A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…

Mathematical Physics · Physics 2007-05-23 Tuncay Aktosun , Vassilis G. Papanicolaou , Vassilis Zisis

We consider the solvability of the direct scattering problem of an obliquely incident time-harmonic electromagnetic wave by a piecewise constant inhomogeneous, penetrable and infinitely long cylinder. We prove the existence and uniqueness…

Analysis of PDEs · Mathematics 2024-02-23 Drossos Gintides , Sotiris Giogiakas , Leonidas Mindrinos

The inverse acoustic scattering problems using multi-frequency backscattering far field patterns at isolated directions are studied. The underlying object could be point like scatterers, small scatterers, extended inhomogeneities and…

Analysis of PDEs · Mathematics 2019-10-18 Xia Ji , Xiaodong Liu

We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…

General Relativity and Quantum Cosmology · Physics 2025-10-28 Jean-Philippe Nicolas , Grigalius Taujanskas