A course on nonlinear waves /
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...
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| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht :
Springer,
[1993]
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| Series: | Nonlinear topics in the mathematical sciences ;
v. 3. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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 Schrdinger 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. 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. |
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| Item Description: | Softcover reprint of the hardcover 1st edition originally published by Kluwer in 1993. Electronic resource. |
| Physical Description: | 1 online resource (xiv, 327 pages :) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 317-322) and index. |
| ISBN: | 9789401121026 (electronic bk.) 9401121028 (electronic bk.) |