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Nonlinear waves and inverse scatteri...

Kuo, Spencer P.,

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Nonlinear waves and inverse scattering transform /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Nonlinear waves and inverse scattering transform // Spencer Kuo.
Author:	Kuo, Spencer P.,
Published:	New Jersey :World Scientific, : c2023.,
Description:	xvi, 181 p. :ill. ;24 cm.
[NT 15003449]:	Nonlinear waves -- Formulation of nonlinear wave equations in plasma -- Characteristics of nonlinear waves -- Inverse scattering transform (IST) -- Basis of inverse scattering transform -- Solitary waves.
Subject:	Nonlinear waves. -
ISBN:	9781800614031

Nonlinear waves and inverse scattering transform /
Kuo, Spencer P.,

Nonlinear waves and inverse scattering transform /Spencer Kuo. - New Jersey :World Scientific,c2023. - xvi, 181 p. :ill. ;24 cm.

Includes bibliographical references (p. 175-177) and index.

Nonlinear waves -- Formulation of nonlinear wave equations in plasma -- Characteristics of nonlinear waves -- Inverse scattering transform (IST) -- Basis of inverse scattering transform -- Solitary waves.

"Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations, which are fundamental to students and researchers. This book provides students, who are familiar with nonlinear waves, methods for solving nonlinear partial differential equations, enabling them to expand their studies into other related areas. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a nonlinear wave course. Chapter 1 introduces "Mode" types in terms of the nonlinear wave forms as well as the generic nonlinear partial differential equations (NLPDEs). Bäcklund transform is introduced to solve different types of NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrodinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST) which addresses the initial value problems of a group NLPDEs. Lax and AKNS equations, which represent a NLPDE, subject to a specific pair of operators are introduced. K-dV equation is adopted to illustrate methods to determine the pair of operators, which lead to two auxiliary equations, one is in the form of linear Schrodinger equation to define the scattering by the solution function of the NLPDE; the second one is a rate equation, which updates the scattering data having the initial condition of the NLPDE as the scatterer. IST then reconstructs the potential function (scatterer) of the Schrodinger equation via the scattering data. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps of applying IST to solve NLPDE for solitary solutions are illustrated in Chapter 6"--

ISBN: 9781800614031US78

LCCN: 2023000255Subjects--Topical Terms:

671954
Nonlinear waves.

LC Class. No.: QA927 / .K863 2023

Dewey Class. No.: 531/.1133

Nonlinear waves and inverse scattering transform /
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020 $a 9781800614031 $q (hardcover) : $c US78
020 $a 1800614039 $q (hardcover)
020 $z 9781800614048 $q (ebook for institutions)
020 $z 9781800614055 $q (ebook for individuals)
035 $a 22969589
040 $a LBSOR $b eng $c LBSOR $d DLC
042 $a pcc
050 0 0 $a QA927 $b .K863 2023
082 0 0 $a 531/.1133 $2 23/eng20230508
100 1 $a Kuo, Spencer P., $e author. $3 3775318
245 1 0 $a Nonlinear waves and inverse scattering transform / $c Spencer Kuo.
260 # $a New Jersey : $b World Scientific, $c c2023.
300 $a xvi, 181 p. : $b ill. ; $c 24 cm.
504 $a Includes bibliographical references (p. 175-177) and index.
505 0 # $a Nonlinear waves -- Formulation of nonlinear wave equations in plasma -- Characteristics of nonlinear waves -- Inverse scattering transform (IST) -- Basis of inverse scattering transform -- Solitary waves.
520 # $a "Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations, which are fundamental to students and researchers. This book provides students, who are familiar with nonlinear waves, methods for solving nonlinear partial differential equations, enabling them to expand their studies into other related areas. The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a nonlinear wave course. Chapter 1 introduces "Mode" types in terms of the nonlinear wave forms as well as the generic nonlinear partial differential equations (NLPDEs). Bäcklund transform is introduced to solve different types of NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrodinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST) which addresses the initial value problems of a group NLPDEs. Lax and AKNS equations, which represent a NLPDE, subject to a specific pair of operators are introduced. K-dV equation is adopted to illustrate methods to determine the pair of operators, which lead to two auxiliary equations, one is in the form of linear Schrodinger equation to define the scattering by the solution function of the NLPDE; the second one is a rate equation, which updates the scattering data having the initial condition of the NLPDE as the scatterer. IST then reconstructs the potential function (scatterer) of the Schrodinger equation via the scattering data. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps of applying IST to solve NLPDE for solitary solutions are illustrated in Chapter 6"-- $c Provided by publisher.
650 # 0 $a Nonlinear waves. $3 671954
650 # 0 $a Inverse scattering transform. $3 560815