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Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with…

Analysis of PDEs · Mathematics 2019-04-18 Yang Liu , Yixian Gao , Jian Zu

Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…

Mathematical Physics · Physics 2015-08-25 Sergei B. Rutkevich , H. W. Diehl

A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. Positive…

Nuclear Theory · Physics 2007-05-23 K. Amos , S. Karataglidis , P. Fraser , D. van der Knijff , J. P. Svenne , L. Canton , G. Pisent

We solve inverse scattering problem for Schr\"odinger operators with compactly supported potentials on the half line. We discretize S-matrix: we take the value of the S-matrix on some infinite sequence of positive real numbers. Using this…

Mathematical Physics · Physics 2020-10-08 Evgeny L. Korotyaev

In this work, we introduce a dispersive N(=2n)-wave interaction problem involving n velocities in two spatial dimensions and one temporal dimension. Exact solutions of the problem are exhibited. This is a generalization of the N-wave…

Exactly Solvable and Integrable Systems · Physics 2020-08-24 Mansur I Ismailov

Inverse scattering problem is discussed for the Maxwell's equations. A reduction of the Maxwell's system to a new Fredholm second-kind integral equation with a {\it scalar weakly singular kernel} is given for electromagnetic (EM) wave…

Analysis of PDEs · Mathematics 2012-06-27 A. G. Ramm

In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…

Nuclear Theory · Physics 2012-05-03 Raymond S. Mackintosh

In this study, the inverse problem of the scattering theory on the half line for a piecewise continuous Sturm-Liouville equation with boundary condition depending quadratic on the spectral parameter is considered. The scattering data of the…

Spectral Theory · Mathematics 2015-02-06 Kh. R. Mamedov , Nida P. Kosar , F. Ayca Cetinkaya

The theory of inverse scattering is developed to study the initial-value problem for the modified matrix Korteweg-de Vries (mmKdV) equation with the $2m\times2m$ $(m\geq 1)$ Lax pairs under the nonzero boundary conditions at infinity. In…

Exactly Solvable and Integrable Systems · Physics 2020-05-04 Jin-Jie Yang , Shou-Fu Tian , Zhi-Qiang Li

A computational model study for complete frequency redistribution linear incoherent two-level atomic radiation trapping in optically dense media using the multiple scattering representation is presented. This model study discuss at length…

Physics Education · Physics 2009-11-13 A. R. Alves-Pereira , E. J. Nunes-Pereira , J. M. G. Martinho , M. N. Berberan-Santos

The following electromagnetism (EM) inverse problem is addressed. It consists in estimating local radioelectric properties of materials recovering an object from global EM scattering measurements, at various incidences and wave frequencies.…

Applications · Statistics 2015-06-12 François Giraud , Pierre Minvielle , Pierre Del Moral

In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…

Numerical Analysis · Mathematics 2023-10-16 Abinand Gopal , Jeremy Hoskins , Vladimir Rokhlin

An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however…

Mathematical Physics · Physics 2007-05-23 S. Kupin , F. Peherstorfer , A. Volberg , P. Yuditskii

With the Marchenko method it is possible to retrieve the wave field inside a medium from its reflection response at the surface. To date, this method has predominantly been applied to naturally occurring materials. In this paper we extend…

Applied Physics · Physics 2020-08-26 Kees Wapenaar

In this paper we suggest a new approach for the multichannel Coulomb scattering problem. The Schr\"{o}dinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The…

Atomic Physics · Physics 2011-07-26 M. V. Volkov , S. L. Yakovlev , E. A. Yarevsky , N. Elander

We extend our previous results of solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, we apply an isosceles triangular-pulse function set for the Marchenko equation input kernel…

Nuclear Theory · Physics 2025-03-18 N. A. Khokhlov

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal…

Spectral Theory · Mathematics 2007-06-13 Iryna Egorova , Johanna Michor , Gerald Teschl

We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…

Analysis of PDEs · Mathematics 2022-10-13 Peijun Li , Xu Wang

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary…

Mathematical Physics · Physics 2016-08-09 Sabina Alazzawi , Gandalf Lechner

The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.

Spectral Theory · Mathematics 2015-12-22 Natalia Bondarenko