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A Course on Nonlinear Waves

  • Book
  • © 1993

Overview

Authors:
  1. Samuel S. Shen

    1. Department of Mathematics, University of Alberta, Edmonton, Canada

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Part of the book series: Nonlinear Topics in the Mathematical Sciences (NTMS, volume 3)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Asymptotic Expansion

    • Samuel S. Shen
    Pages 1-23

  3. Hyperbolic Waves

    • Samuel S. Shen
    Pages 25-51

  4. Water Waves

    • Samuel S. Shen
    Pages 53-74

  5. Scattering and Inverse Scattering

    • Samuel S. Shen
    Pages 75-122

  6. Burgers Equation

    • Samuel S. Shen
    Pages 123-145

  7. Forced KdV Equation

    • Samuel S. Shen
    Pages 147-187

  8. Sine-Gordon and Nonlinear Schrödinger

    • Samuel S. Shen
    Pages 189-217

  9. Selected Examples of Flow Instabilities

    • Samuel S. Shen
    Pages 219-246

  10. Wave Interactions and X-Ray Crystallography

    • Samuel S. Shen
    Pages 247-275

  11. Back Matter

    Pages 277-329
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Alberta, Edmonton, Canada

    Samuel S. Shen

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