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Nonlinear periodic waves and their modulations : an introductory course /
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
©2000.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kamchatnov, A. M. |q (Anatoliĭ Mikhaĭlovich) | |
| 245 | 1 | 0 | |a Nonlinear periodic waves and their modulations : |b an introductory course / |c A.M. Kamchatnov. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2000. | ||
| 300 | |a 1 online resource (xiv, 383 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 504 | |a Includes bibliographical references (pages 373-380) and index. | ||
| 505 | 0 | |a Introduction and basic concepts -- Nonlinear wave equations in physics -- Whitham theory of modulations -- Complete integrability of nonlinear wave equations -- Periodic solutions -- Dissipationless shock wave -- Nonlinear theory of modulational instability. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics. This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Nonlinear waves. | |
| 650 | 0 | |a Wave-motion, Theory of. | |
| 650 | 0 | |a Solitons. | |
| 650 | 6 | |a Ondes non linéaires. | |
| 650 | 6 | |a Théorie du mouvement ondulatoire. | |
| 650 | 6 | |a Solitons. | |
| 650 | 7 | |a SCIENCE |x Waves & Wave Mechanics. |2 bisacsh | |
| 650 | 7 | |a Nonlinear waves. |2 fast |0 (OCoLC)fst01038821 | |
| 650 | 7 | |a Solitons. |2 fast |0 (OCoLC)fst01125558 | |
| 650 | 7 | |a Wave-motion, Theory of. |2 fast |0 (OCoLC)fst01172888 | |
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| 776 | 0 | 8 | |i Print version: |a Kamchatnov, A.M. (Anatoliĭ Mikhaĭlovich). |t Nonlinear periodic waves and their modulations. |d Singapore ; River Edge, NJ : World Scientific, ©2000 |z 981024407X |w (DLC) 2005297755 |w (OCoLC)45705714 |
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