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An example of full solution of the inverse scattering problem on the half line is presented. For this purpose, a simple analytically solvable model system (Morse potential) is used, which is expected to be a reasonable approximation to a…

Quantum Physics · Physics 2015-01-20 Matti Selg

We obtain a nonperturbative, analytical solution to integral equation of scattering theory by assuming the field within the scattering object is a spherical wave with a scattering amplitude equal to that of the far field. This approximation…

Classical Physics · Physics 2018-09-26 Brian Slovick , Srini Krishnamurthy

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete…

Spectral Theory · Mathematics 2008-11-20 Anne Boutet de Monvel , Iryna Egorova , Gerald Teschl

The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…

Mathematical Physics · Physics 2011-11-28 Tamas Palmai , Barnabas Apagyi

In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and…

Mathematical Physics · Physics 2024-07-24 Ya-Hui Liu , Rui Guo , Jian-Wen Zhang

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

Analysis of PDEs · Mathematics 2025-07-02 Jianliang Li , Peijun Li , Xu Wang , Guanlin Yang

In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…

Numerical Analysis · Mathematics 2019-10-23 Ziqing Xie , Rui Zhang , Bo Wang , Li-lian Wang

We study the direct and inverse scattering problem for the one-dimensional Schr\"odinger equation with steplike potentials. We give necessary and sufficient conditions for the scattering data to correspond to a potential with prescribed…

Spectral Theory · Mathematics 2017-08-04 Iryna Egorova , Zoya Gladka , Till Luc Lange , Gerald Teschl

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi

We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total…

Mathematical Physics · Physics 2026-05-25 John C. Schotland , Shenwen Yu

In this work we shall review the (phased) inverse scattering problem and then pursue the phaseless reconstruction from far-field data with the help of the concept of scattering coefficients. We perform sensitivity, resolution and stability…

Numerical Analysis · Mathematics 2015-10-15 Habib Ammari , Yat Tin Chow , Jun Zou

This paper is mainly concerned with the inverse scattering problem of determining the unknown potential for the classical Schr\"odinger equation in two and three dimensions. We establish the increasing stability of the inverse scattering…

Analysis of PDEs · Mathematics 2023-06-21 Jian Zhai , Yue Zhao

We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…

Analysis of PDEs · Mathematics 2018-07-16 Juan A. Barceló , Carlos Castro , Teresa Luque , Mari Cruz Vilela

We consider the scattering of time-harmonic plane waves by a compactly supported inhomogeneous scattering obstacle governed by the Helmholtz equation. Given far field observations of the scattered fields corresponding to plane wave incident…

Numerical Analysis · Mathematics 2026-02-03 Roland Griesmaier , Bastian Harrach , Jianli Xiang

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

This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…

Numerical Analysis · Mathematics 2024-12-20 Xiaoli Liu , Ruming Zhang

We discuss the inverse uniqueness problem in phaseless scattering by counting the zeros of its modulus of the scattering amplitude. The phase linearization of scattered wave field disturbs the originally uniform distribution of the zero…

Spectral Theory · Mathematics 2016-06-06 Lung-Hui Chen

In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading…

Mathematical Physics · Physics 2020-05-22 Ricardo Weder , Dimitri Yafaev

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the…

solv-int · Physics 2007-05-23 T. Tsuchida , H. Ujino , M. Wadati

This paper investigates the inverse biharmonic scattering problems of identifying the shape and location of the obstacle with phased and phaseless measurement data. A direct imaging method based on reverse time migration is proposed for…

Analysis of PDEs · Mathematics 2026-05-12 Tielei Zhu , Zhihao Ge