An Introduction to the Mathematical Theory of Waves

Paperback | 1 January 1999

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"Linear and nonlinear waves are a central part of the theory of PDEs. This book begins with a description of one-dimensional waves and their visualization through computer-aided techniques. Next, traveling waves are covered, such as solitary waves for the Klein-Gordon and KdV equations. Finally, the author gives a lucid discussion of waves arising from conservation laws, including shock and rarefaction waves. As an application, interesting models of traffic flow are used to illustrate conservation laws and wave phenomena." "This book is based on a course given by the author at the IAS/Park City Mathematics Institute. It is suitable for independent study by undergraduate students in mathematics, engineering, and science programs."--BOOK JACKET. Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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Introduction
Introduction to waves
A mathematical representation of waves
Partial differential equation
Traveling and standing waves: Traveling waves
The Korteweg-de Vries equation
The Sine-Gordon equation
The wave equation D'Alembert's solution of the wave equation
Vibrations of a semi-infinite string
Characteristic lines of the wave equation
Standing wave solutions of the wave equation
Standing waves of a nonhomogeneous string
Superposition of standing waves
Fourier series and the wave equation
Waves in conservation laws: Conservation laws
Examples of conservation laws
The method of characteristics
Gradient catastrophes and breaking times
Shock waves Shock wave example: Traffic at a red light
Shock waves and the viscosity method
Rarefaction waves An example with rarefaction and shock waves
Nonunique solutions and the entropy condition
Weak solutions of conservation laws
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

An Introduction to the Mathematical Theory of Waves

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