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Inverse scattering problems and thei...

Vu, Pham Loi.

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Inverse scattering problems and their application to non-linear integrable equations /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Inverse scattering problems and their application to non-linear integrable equations // Pham Loi Vu.
Author:	Vu, Pham Loi.
Published:	Boca Raton :CRC Press, Taylor & Francis Group, : c2020.,
Description:	xxvi, 388 p. :port. ;25 cm.
Notes:	"A Chapman & Hall book"--Title page.
Subject:	Inverse problems (Differential equations) -
ISBN:	9780367334895

Inverse scattering problems and their application to non-linear integrable equations /
Vu, Pham Loi.

Inverse scattering problems and their application to non-linear integrable equations /Pham Loi Vu. - Boca Raton :CRC Press, Taylor & Francis Group,c2020. - xxvi, 388 p. :port. ;25 cm. - Monographs & research notes in mathematics. - Monographs & research notes in mathematics..

"A Chapman & Hall book"--Title page.

Includes bibliographical references (p. 375-385) and index.

"Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. Solving the associated IVP or IBVP for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values (BVs) are calculated, then the time-dependent scattering data (SD) are constructed from the given initial and boundary conditions. The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the ISM. The application of ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM."--Provided by publisher.

ISBN: 9780367334895GBP140.00

LCCN: 2019949580Subjects--Topical Terms:

566558
Inverse problems (Differential equations)

LC Class. No.: QA371 / .V8 2020

Dewey Class. No.: 515.357

Inverse scattering problems and their application to non-linear integrable equations /
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100 1 $a Vu, Pham Loi. $3 3470119
245 1 0 $a Inverse scattering problems and their application to non-linear integrable equations / $c Pham Loi Vu.
260 # $a Boca Raton : $b CRC Press, Taylor & Francis Group, $c c2020.
300 $a xxvi, 388 p. : $b port. ; $c 25 cm.
490 1 $a Monographs & research notes in mathematics
500 $a "A Chapman & Hall book"--Title page.
504 $a Includes bibliographical references (p. 375-385) and index.
520 # $a "Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. Solving the associated IVP or IBVP for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values (BVs) are calculated, then the time-dependent scattering data (SD) are constructed from the given initial and boundary conditions. The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the ISM. The application of ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM."--Provided by publisher.
650 # 0 $a Inverse problems (Differential equations) $3 566558
650 # 0 $a Nonlinear integral equations. $3 811855
650 # 0 $a Scattering (Mathematics) $3 596281
830 0 $a Monographs & research notes in mathematics. $3 3470120