A Course on Nonlinear Waves: 3 (Nonlinear Topics in the Mathematical Sciences, 3) - Hardcover

Shen, S.S.

Hardcover

ISBN 10: 0792322924 ISBN 13: 9780792322924

Publisher: Springer, 1993

Synopsis

The aim of this book is to give a self-contained introduction to the mathe­ matical analysis and physical explanations of some basic nonlinear wave phe­ nomena. This volume grew out of lecture notes for graduate courf;!es which I gave at the University of Alberta, the University of Saskatchewan, ·and Texas A&M University. As an introduction it is not intended to be exhaustive iQ its choice of material, but rather to convey to interested readers a basic; yet practical, methodology as well as some of the more important results obtained since the 1950's. Although the primary purpose of this volume is to serve as a textbook, it should be useful to anyone who wishes to understand or conduct research into nonlinear waves. Here, for the first time, materials on X-ray crystallography and the forced Korteweg-de Vries equation are incorporated naturally into a textbook on non­ linear waves. Another characteristic feature of the book is the inclusion of four symbolic calculation programs written in MATHEMATICA. They emphasize outcomes rather than numerical methods and provide certain symbolic and nu­ merical results related to solitons. Requiring only one or two commands to run, these programs have user-friendly interfaces. For example, to get the explicit expression of the 2-soliton of the Korteweg-de Vries equation, one only needs to type in soliton[2] when using the program solipac.m.

About this title

Synopsis

This volume presents a carefully written introduction to nonlinear waves in the natural sciences and engineering. It contains many classical results as well as more recent results, dealing with topics such as the forced Korteweg-de Vries equation and material relating to X-ray crystallography. The volume contains nine chapters. Chapter 1 concerns asymptotics and nonlinear ordinary differential equations. Conservation laws are discussed in Chapter 2, and Chapter 3 considers water waves. The scattering and inverse scattering method is described in Chapter 4, which also contains a full explanation of using the inverse scattering method for finding 1-, 2- and 3-soliton solutions of the Korteweg-de Vries equation.After dealing with the Burgers equation in Chapter 5, Chapter 6 discusses the forced Korteweg-de Vries equations. Here the emphasis is on steady-state bifurcations and unsteady-state periodic soliton generation. The Sine-Gordon and nonlinear Schrodinger equations are the subject of Chapter 7. The final two chapters consider wave instability and resonance. Every chapter contains problems and exercises, together with guidance for their solution.

The volume concludes with some appendices which describe symbolic derivations of certain results on solitons. Several user-friendly Mathematica packages are included. The prerequisite for using this book is a background knowledge of basic physics, linear algebra and differential equations. It is intended for graduates and researchers in mathematics, physics and engineering wishing to have a good introduction to nonlinear wave theory and its applications. This volume is also highly recommended as a course book.

Edition details

• Publisher: Springer
• Publication date: 1993
• ISBN 10: 0792322924
• ISBN 13: 9780792322924
• Binding: Hardcover
• Language: English
• Number of pages: 341