國立虎尾科技大學 |

Direct and Inverse Scattering for the Matrix Schrödinger Equation

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Direct and Inverse Scattering for the Matrix Schrödinger Equation/ by Tuncay Aktosun, Ricardo Weder.
Author:	Aktosun, Tuncay.
other author:	Weder, Ricardo.
Description:	XIII, 624 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-030-38431-9
ISBN:	9783030384319

Direct and Inverse Scattering for the Matrix Schrödinger Equation
Aktosun, Tuncay.

Direct and Inverse Scattering for the Matrix Schrödinger Equation[electronic resource] /by Tuncay Aktosun, Ricardo Weder. - 1st ed. 2021. - XIII, 624 p. 1 illus.online resource. - Applied Mathematical Sciences,2032196-968X ;. - Applied Mathematical Sciences,191.

The matrix Schrödinger 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 Schrödinger 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:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

Direct and Inverse Scattering for the Matrix Schrödinger Equation
LDR:03525nam a22004095i 4500 001 1049074
003 DE-He213
005 20210819113448.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030384319 $9 978-3-030-38431-9
024 7 $a 10.1007/978-3-030-38431-9 $2 doi
035 $a 978-3-030-38431-9
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
100 1 $a Aktosun, Tuncay. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1353108
245 1 0 $a Direct and Inverse Scattering for the Matrix Schrödinger Equation $h [electronic resource] / $c by Tuncay Aktosun, Ricardo Weder.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XIII, 624 p. 1 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Applied Mathematical Sciences, $x 2196-968X ; $v 203
505 0 $a The matrix Schrödinger 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 Schrödinger 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.
650 0 $a Partial differential equations. $3 1102982
650 0 $a Functional analysis. $3 527706
650 0 $a Quantum physics. $3 1179090
650 0 $a Mathematical physics. $3 527831
650 1 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Quantum Physics. $3 671960
650 2 4 $a Mathematical Physics. $3 786661
700 1 $a Weder, Ricardo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1353109
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030384302
776 0 8 $i Printed edition: $z 9783030384326
776 0 8 $i Printed edition: $z 9783030384333
830 0 $a Applied Mathematical Sciences, $x 0066-5452 ; $v 191 $3 1254006
856 4 0 $u https://doi.org/10.1007/978-3-030-38431-9
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)