Multidimensional Inverse Scattering for First Order Systems.

In this paper, inverse scattering problems for a system of diﬀerential equations of the ﬁrst order are considered. The Marchenko approach is used to solve the inverse scattering problem. The system of Marchenko integral equations is reduced to a linear system of algebraic equations such that the solution of the resulting system yields to the unknown coeﬃcients of the system of ﬁrst-order diﬀerential equations. Illustrative examples are provided to demonstrate the preciseness and eﬀectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.

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Scattering and inverse scattering for first-order systems: II

Inverse Problems ◽

10.1088/0266-5611/3/4/009 ◽

1987 ◽

Vol 3 (4) ◽

pp. 577-593 ◽

Cited By ~ 58

Author(s):

R Beals ◽

R R Coifman

Keyword(s):

Inverse Scattering ◽

First Order

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A stationary approach to inverse scattering for schrodinger operators with first order perturbation

Communications in Partial Differential Equations ◽

10.1080/03605309708821273 ◽

1997 ◽

Vol 22 (3-4) ◽

pp. 527-553 ◽

Cited By ~ 11

Author(s):

Nicoleau Francois

Keyword(s):

Inverse Scattering ◽

Schrödinger Operators ◽

Order Perturbation ◽

Schrodinger Operators ◽

First Order ◽

Stationary Approach ◽

First Order Perturbation

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Inverse scattering for the higher order Schrödinger operator with a first order perturbation

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2018-0036 ◽

2019 ◽

Vol 27 (3) ◽

pp. 409-427

Author(s):

Hua Huang ◽

Zhiwen Duan ◽

Quan Zheng

Keyword(s):

Inverse Scattering ◽

Schrödinger Operator ◽

Scattering Matrix ◽

Higher Order ◽

Zero Order ◽

Schrodinger Operator ◽

Scattering Problems ◽

First Order ◽

Fixed Energy ◽

First Order Perturbation

Abstract This paper concerns inverse scattering problems at a fixed energy for the higher order Schrödinger operator with the first order perturbed potentials in dimensions {n\geq 3} . We show that the scattering matrix uniquely determines the first order perturbed potentials and the zero order potentials.

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