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A Course on Nonlinear Waves : Nonlinear Topics in the Mathematical Sciences - Samuel S. Shen

A Course on Nonlinear Waves

Nonlinear Topics in the Mathematical Sciences


Published: 30th June 1993
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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 Schr”dinger 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.

Asymptotic Expansionp. 1
Hyperbolic Wavesp. 25
Water Wavesp. 53
Scattering and Inverse Scatteringp. 75
Burgers Equationp. 123
Forced KdV Equationp. 147
Sine-Gordon and Nonlinear Schrodingerp. 189
Selected Examples of Flow Instabilitiesp. 219
Wave Interactions and X-Ray Crystallographyp. 247
Appendix A: KdV Solitons via Inverse Scatteringp. 277
Appendix B: KdV Solitons via Backlund Transformp. 283
Appendix C: Derivation of the Stationary KdVp. 309
Bibliographyp. 317
Indexp. 323
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792322924
ISBN-10: 0792322924
Series: Nonlinear Topics in the Mathematical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 327
Published: 30th June 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 2.54
Weight (kg): 0.77