Nonlinear Waves and Inverse Scattering Transform

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, Kortewegde 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.

Contents:

• Nonlinear Waves
• Formulation of Nonlinear Wave Equations in Plasma
• Characteristics of Nonlinear Waves
• Inverse Scattering Transform (IST)
• Basis of Inverse Scattering Transform
• Solitary Waves

Readership: Graduate and senior graduate courses on nonlinear waves, also relevant as a reference book for researchers, research labs and academic institutes.
Key Features:

• There are many journal articles, monographs, and advanced reference books in this subject area, but a book introducing this topic area in a methodical sense is not available
• This book is presented from the physics and engineering points of view, rather than from the mathematics point of view, making it easier for physics and engineering students to navigate the material
• The selection of topics and the focus given to each provide essential materials for a lecturer to cover the bases in a one-semester nonlinear wave course

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