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Nonlinear Wave Dynamics: Complexity and Simplicity (Texts in the Mathematical Sciences) - Softcover

 
9789048148332: Nonlinear Wave Dynamics: Complexity and Simplicity (Texts in the Mathematical Sciences)

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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.

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9780792345084: Nonlinear Wave Dynamics: Complexity and Simplicity (Texts in the Mathematical Sciences, 17)

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ISBN 10:  0792345088 ISBN 13:  9780792345084
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Engelbrecht, J.
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J. Engelbrecht
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Paperback. Condition: new. Paperback. The general idea advocated in this book is to start from complicated mathematical models describing wave motion as it results from the rules of continuum mechanics and then to find a simpler viewpoint that still keeps everything essential preserved. Special attention is paid to the description of the sources of nonlinearities. The complexities in modelling are demonstrated by several examples including solitons, propagating instabilities and waves in waveguides. The selected case studies show some unconventional approaches in order to explain the richness of nonlinear wave motion. The final chapters are of more general character, including the essays on nonlinearity, beauty, and complexity. In this way, the thread of the analysis is the following: simple basic arguments result in a complicated theory that, in turn, needs certain simplifications in order to grasp the physical phenomena involved. What makes this book special compared to other books in the field is that all the examples are cast into a general philosophical network of complexity and simplicity.Audience: This volume will be of interest to researchers and students whose work involves mathematical modelling of wave phenomena. At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9789048148332

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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 200 pp. Englisch. Seller Inventory # 9789048148332

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Condition: New. Series: Texts in the Mathematical Sciences. Num Pages: 185 pages, biography. BIC Classification: PBKJ; PBW; TGB; TGMD4. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 10. Weight in Grams: 314. . 2010. 1st ed. Softcover of orig. ed. 1997. Paperback. . . . . Seller Inventory # V9789048148332

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