Nonlinear Wave Dynamics : Complexity and Simplicity / by Jüri Engelbrecht
(Kluwer Texts in the Mathematical Sciences ; 17)
| データ種別 | 電子ブック |
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| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1997 |
| 本文言語 | 英語 |
| 大きさ | XIV, 185 p : online resource |
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| 内容注記 | 1 Introduction: basic wave theory 2 Essential continuum mechanics 3 Nonlinearities: cornerstones for complexity 4 Nonlinear wave dynamics: mathematical models 5 Wave phenomena: complexities in modelling 6 Selected case studies 7 Essays: what is all that about 8 Final remarks: complexity of wave motion References |
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| 一般注記 | At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc |
| 著者標目 | *Engelbrecht, Jüri author SpringerLink (Online service) |
| 件 名 | LCSH:Engineering LCSH:Partial differential equations LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Continuum mechanics LCSH:Vibration LCSH:Dynamical systems LCSH:Dynamics FREE:Engineering FREE:Vibration, Dynamical Systems, Control FREE:Partial Differential Equations FREE:Continuum Mechanics and Mechanics of Materials FREE:Applications of Mathematics |
| 分 類 | DC23:620 |
| 巻冊次 | ISBN:9789401588911 
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| ISBN | 9789401588911 |
| URL | http://dx.doi.org/10.1007/978-94-015-8891-1 |
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