Nonlinear periodic waves and their modulations: an introductory course
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2000
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 373-380) and index 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 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 |
| Beschreibung: | 1 Online-Ressource (xiv, 383 p.) |
| ISBN: | 9789810244071 9789812792259 981024407X 9812792252 |
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| 100 | 1 | |a Kamchatnov, A. M., (Anatoliĭ Mikhaĭlovich) |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear periodic waves and their modulations |b an introductory course |c A.M. Kamchatnov |
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| 500 | |a Includes bibliographical references (p. 373-380) and index | ||
| 500 | |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 | ||
| 500 | |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 | ||
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Datensatz im Suchindex
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| author | Kamchatnov, A. M., (Anatoliĭ Mikhaĭlovich) |
| author_facet | Kamchatnov, A. M., (Anatoliĭ Mikhaĭlovich) |
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| discipline | Physik |
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| isbn | 9789810244071 9789812792259 981024407X 9812792252 |
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| spelling | Kamchatnov, A. M., (Anatoliĭ Mikhaĭlovich) Verfasser aut Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov Singapore World Scientific c2000 1 Online-Ressource (xiv, 383 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 373-380) and index 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 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 Teoria de campos e ondas larpcal SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear waves fast Solitons fast Wave-motion, Theory of fast Nonlinear waves Wave-motion, Theory of Solitons http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514193 Aggregator Volltext |
| spellingShingle | Kamchatnov, A. M., (Anatoliĭ Mikhaĭlovich) Nonlinear periodic waves and their modulations an introductory course Teoria de campos e ondas larpcal SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear waves fast Solitons fast Wave-motion, Theory of fast Nonlinear waves Wave-motion, Theory of Solitons |
| title | Nonlinear periodic waves and their modulations an introductory course |
| title_auth | Nonlinear periodic waves and their modulations an introductory course |
| title_exact_search | Nonlinear periodic waves and their modulations an introductory course |
| title_full | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_fullStr | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_full_unstemmed | Nonlinear periodic waves and their modulations an introductory course A.M. Kamchatnov |
| title_short | Nonlinear periodic waves and their modulations |
| title_sort | nonlinear periodic waves and their modulations an introductory course |
| title_sub | an introductory course |
| topic | Teoria de campos e ondas larpcal SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear waves fast Solitons fast Wave-motion, Theory of fast Nonlinear waves Wave-motion, Theory of Solitons |
| topic_facet | Teoria de campos e ondas SCIENCE / Waves & Wave Mechanics Nonlinear waves Solitons Wave-motion, Theory of |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=514193 |
| work_keys_str_mv | AT kamchatnovamanatoliimikhailovich nonlinearperiodicwavesandtheirmodulationsanintroductorycourse |