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Mathematical Studies in Nonlinear Wave Propagation

2005 Mathematics
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Release : 2005
Genre : Mathematics
Kind : eBook
Book Rating : 499/5 ( reviews)

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Book Synopsis Mathematical Studies in Nonlinear Wave Propagation by : Dominic P. Clemence

Download or read book Mathematical Studies in Nonlinear Wave Propagation written by Dominic P. Clemence. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: Lively discussions and stimulating research were part of a five-day conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and CBMS. This volume is a collection of lectures and papers stemming from that event. Leading experts present dynamical systems and chaos, scattering and spectral theory, nonlinear wave equations, optimal control, optical waveguide design, and numerical simulation. The book is suitable for a diverse audience of mathematical specialists interested in fiber optic communications and other nonlinear phenomena. It is also suitable for engineers and other scientists interested in the mathematics of nonlinear wave propagation.

Nonlinear Wave Equations

2021-05-30 Mathematics
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Release : 2021-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 724/5 ( reviews)

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Book Synopsis Nonlinear Wave Equations by : Satyanad Kichenassamy

Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy. This book was released on 2021-05-30. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Mathematics of Wave Propagation

2021-01-12 Mathematics
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Release : 2021-01-12
Genre : Mathematics
Kind : eBook
Book Rating : 378/5 ( reviews)

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Book Synopsis Mathematics of Wave Propagation by : Julian L. Davis

Download or read book Mathematics of Wave Propagation written by Julian L. Davis. This book was released on 2021-01-12. Available in PDF, EPUB and Kindle. Book excerpt: Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.

Recent Mathematical Methods in Nonlinear Wave Propagation

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 657/5 ( reviews)

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Book Synopsis Recent Mathematical Methods in Nonlinear Wave Propagation by : Guy Boillat

Download or read book Recent Mathematical Methods in Nonlinear Wave Propagation written by Guy Boillat. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

Nonlinear Wave Dynamics

2013-04-17 Technology & Engineering
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Release : 2013-04-17
Genre : Technology & Engineering
Kind : eBook
Book Rating : 910/5 ( reviews)

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Book Synopsis Nonlinear Wave Dynamics by : J. Engelbrecht

Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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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