Nonlinear Waves And Inverse Scattering Transform
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A01=Spencer P Kuo
AKNS Pair and Equation
Author_Spencer P Kuo
Backlund Transform
BAfA?cklund Transform
Burgers Equation
Category=PHK
Cole-Hopf Transformation
Collapse of Nonlinear Waves
Conservation Laws
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Gelfand-Levitan-Marchenko Integral Equation
Hamilton's Equation of Motion
Hamiltonian
Inverse Scattering Transform (IST)
Korteweg-de Vries (K-dV) Equation
Langmuir Collapse
Lax Pair and Equation
Miura Transformation
Mode
Nonlinear Partial Differential Equations (NLPDEs)
Nonlinear Schrodinger Equation
Nonlinear Waves
Sine-Gordon Equation
Solitary Wave
Soliton
Variance Identity
Virial Theorem
Product details
- ISBN 9781800614031
- Publication Date: 21 Jul 2023
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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 (NLPDEs). This book was prepared to familiarize students with nonlinear waves and methods of solving NLPDEs, which will enable them to expand their studies into related areas. The selection of topics and the focus given to each provide essential materials for a lecturer teaching a nonlinear wave course.Chapter 1 introduces "mode" types in nonlinear systems as well as Bäcklund transform, an indispensable technique to solve generic NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST), addressing the initial value problems of a group of NLPDEs. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps for applying IST to solve NLPDEs for solitary solutions are illustrated in Chapter 6.
