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Related papers: The generalized Marchenko method in the inverse sc…

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Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong.Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple…

Applied Physics · Physics 2020-06-09 Kees Wapenaar , Christian Reinicke

Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…

Computational Physics · Physics 2025-12-12 Olivia Tsang , Owen Melia , Vasileios Charisopoulos , Jeremy Hoskins , Yuehaw Khoo , Rebecca Willett

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

The Marchenko method retrieves the responses to virtual sources in the Earth's subsurface from reflection data at the surface, accounting for all orders of multiple reflections. The method is based on two integral representations for…

Geophysics · Physics 2020-11-25 Johno van IJsseldijk , Kees Wapenaar

We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of…

Nuclear Theory · Physics 2018-09-13 Mahmut Elbistan , Pengming Zhang , Janos Balog

We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…

Quantum Physics · Physics 2015-06-17 Ali Mostafazadeh

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

A generalised inverse scattering method has been developed for arbitrary n dimensional Lax equations. Subsequently, the method has been used to obtain N soliton solutions of a vector higher order nonlinear Schrodinger equation, proposed by…

solv-int · Physics 2009-10-31 Sasanka Ghosh , Sudipta Nandy

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

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its…

General Relativity and Quantum Cosmology · Physics 2009-10-31 S. Micciche , J. B. Griffiths

We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…

Analysis of PDEs · Mathematics 2024-04-23 Changxing Miao , Ruipeng Shen , Tengfei Zhao

The demand for inverse design is increasing as the ability to fabricate sub-10 nm features expands the design space by orders of magnitude. Efficient inverse design benefits from differentiable models of light-structure interaction. While…

Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 M. Boiti , F. Pempinelli , A. K. Pogrebkov , B. Prinari

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 Marchenko method retrieves the responses to virtual sources in the subsurface, accounting for all orders of multiples. The method is based on two integral representations for focusing and Green's functions. In discretized form these…

Geophysics · Physics 2020-03-25 Johno van IJsseldijk , Kees Wapenaar

Using a parameterisation of general self-adjoint boundary conditions in terms of Lagrange planes we propose a scheme for factorising the matrix Schroedinger operator and hence construct a Darboux transformation an interesting feature of…

Mathematical Physics · Physics 2007-05-23 M. Harmer

A numerical method to solve the direct scattering problem for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schroedinger equation is proposed. The method involves the numerical solution of Volterra…

Numerical Analysis · Mathematics 2015-02-17 Luisa Fermo , Cornelis van der Mee , Sebastiano Seatzu

The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…

Probability · Mathematics 2012-08-29 Jeffrey J. Hunter

We give a new proof of well posedness of the inverse modified scattering problem for the Vlasov--Poisson system: for every suitable scattering profile there exists a solution of Vlasov--Poisson which disperses and scatters, in a modified…

Analysis of PDEs · Mathematics 2024-04-25 Volker Schlue , Martin Taylor

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…

Mathematical Physics · Physics 2007-05-23 S. Gutman , A. G. Ramm , W. Scheid