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Direct and inverse scattering for th...

Aktosun, Tuncay.

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Direct and inverse scattering for the Matrix Schrodinger equation

Record Type:	Electronic resources : Monograph/item
Title/Author:	Direct and inverse scattering for the Matrix Schrodinger equation/ by Tuncay Aktosun, Ricardo Weder.
Author:	Aktosun, Tuncay.
other author:	Weder, Ricardo.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xiii, 624 p. :ill., digital ;24 cm.
[NT 15003449]:	The matrix Schrodinger equation and the characterization of the scattering data -- Direct scattering I -- Direct scattering II -- Inverse scattering -- Some explicit examples -- Mathematical preliminaries.
Contained By:	Springer eBooks
Subject:	Scattering (Mathematics) -
Online resource:	https://doi.org/10.1007/978-3-030-38431-9
ISBN:	9783030384319

Direct and inverse scattering for the Matrix Schrodinger equation
Aktosun, Tuncay.

Direct and inverse scattering for the Matrix Schrodinger equation[electronic resource] /by Tuncay Aktosun, Ricardo Weder. - Cham :Springer International Publishing :2021. - xiii, 624 p. :ill., digital ;24 cm. - Applied mathematical sciences,v.2030066-5452 ;. - Applied mathematical sciences ;v.203..

The matrix Schrodinger equation and the characterization of the scattering data -- Direct scattering I -- Direct scattering II -- Inverse scattering -- Some explicit examples -- Mathematical preliminaries.

Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrodinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.

ISBN: 9783030384319

Standard No.: 10.1007/978-3-030-38431-9doiSubjects--Topical Terms:

596281
Scattering (Mathematics)

LC Class. No.: QA329 / .A57 2021

Dewey Class. No.: 515.353

Direct and inverse scattering for the Matrix Schrodinger equation
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245 1 0 $a Direct and inverse scattering for the Matrix Schrodinger equation $h [electronic resource] / $c by Tuncay Aktosun, Ricardo Weder.
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490 1 $a Applied mathematical sciences, $x 0066-5452 ; $v v.203
505 0 $a The matrix Schrodinger equation and the characterization of the scattering data -- Direct scattering I -- Direct scattering II -- Inverse scattering -- Some explicit examples -- Mathematical preliminaries.
520 $a Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for the matrix Schrodinger equation on the half line with the general selfadjoint boundary condition. The existence, uniqueness, construction, and characterization aspects are treated with mathematical rigor, and physical insight is provided to make the material accessible to mathematicians, physicists, engineers, and applied scientists with an interest in scattering and inverse scattering. The material presented is expected to be useful to beginners as well as experts in the field. The subject matter covered is expected to be interesting to a wide range of researchers including those working in quantum graphs and scattering on graphs. The theory presented is illustrated with various explicit examples to improve the understanding of scattering and inverse scattering problems. The monograph introduces a specific class of input data sets consisting of a potential and a boundary condition and a specific class of scattering data sets consisting of a scattering matrix and bound-state information. The important problem of the characterization is solved by establishing a one-to-one correspondence between the two aforementioned classes. The characterization result is formulated in various equivalent forms, providing insight and allowing a comparison of different techniques used to solve the inverse scattering problem. The past literature treated the type of boundary condition as a part of the scattering data used as input to recover the potential. This monograph provides a proper formulation of the inverse scattering problem where the type of boundary condition is no longer a part of the scattering data set, but rather both the potential and the type of boundary condition are recovered from the scattering data set.
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