Rogue and Shock Waves in Nonlinear Dispersive Media

Rogue and Shock Waves in Nonlinear Dispersive Media

Author: Miguel Onorato

Publisher: Springer

Published: 2016-09-19

Total Pages: 376

ISBN-13: 331939214X

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This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.


Nonlinear Random Waves

Nonlinear Random Waves

Author: Vladimir V Konotop

Publisher: World Scientific

Published: 1994-07-26

Total Pages: 309

ISBN-13: 9814502154

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This book is mainly devoted to the dynamics of the one-dimensional nonlinear stochastic waves. It contains a description of the basic mathematical tools as well as the latest results in the following fields: exactly integrable nonlinear stochastic equations, dynamics of the nonlinear waves in random media, evolution of the random waves in nonlinear media and the basic concepts of the numerical simulations in nonlinear random wave dynamics. A brief outline of the localization phenomenon in the nonlinear medium is also given. The approach is interdisciplinary describing the general methods with application to specific examples. The results presented may be useful for those who work in the areas of solid state physics, hydrodynamics, nonlinear optics, plasma physics, mathematical models of micromolecules and biological structures, …etc. Since many results are based on the inverse scattering technique, perturbation theory for solitons and the methods of the statistical radiophysics, the terminology of the respective fields is used.


Nonlinear Random Waves

Nonlinear Random Waves

Author: Vladimir V. Konotop

Publisher: World Scientific

Published: 1994

Total Pages: 312

ISBN-13: 9789810217259

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This book is mainly devoted to the dynamics of the one-dimensional nonlinear stochastic waves. It contains a description of the basic mathematical tools as well as the latest results in the following fields: exactly integrable nonlinear stochastic equations, dynamics of the nonlinear waves in random media, evolution of the random waves in nonlinear media and the basic concepts of the numerical simulations in nonlinear random wave dynamics. A brief outline of the localization phenomenon in the nonlinear medium is also given. The approach is interdisciplinary describing the general methods with application to specific examples. The results presented may be useful for those who work in the areas of solid state physics, hydrodynamics, nonlinear optics, plasma physics, mathematical models of micromolecules and biological structures, ?etc. Since many results are based on the inverse scattering technique, perturbation theory for solitons and the methods of the statistical radiophysics, the terminology of the respective fields is used.


Waves and Structures in Nonlinear Nondispersive Media

Waves and Structures in Nonlinear Nondispersive Media

Author: Sergey Nikolaevich Gurbatov

Publisher: Springer Science & Business Media

Published: 2012-03-23

Total Pages: 477

ISBN-13: 3642236170

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"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is the Full member of Russian Academy of Sciences, the head of Department at Moscow University and Professor at BTH (Sweden). Dr. Saichev A.I. is the Professor at the Faculty of Radiophysics of Nizhny Novgorod State University, Professor of ETH Zürich.


Wave Propagation and Time Reversal in Randomly Layered Media

Wave Propagation and Time Reversal in Randomly Layered Media

Author: Jean-Pierre Fouque

Publisher: Springer Science & Business Media

Published: 2007-06-30

Total Pages: 623

ISBN-13: 0387498087

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The content of this book is multidisciplinary by nature. It uses mathematical tools from the theories of probability and stochastic processes, partial differential equations, and asymptotic analysis, combined with the physics of wave propagation and modeling of time reversal experiments. It is addressed to a wide audience of graduate students and researchers interested in the intriguing phenomena related to waves propagating in random media. At the end of each chapter there is a section of notes where the authors give references and additional comments on the various results presented in the chapter.


Geophysical Fluid Dynamics

Geophysical Fluid Dynamics

Author: Vladimir Zeitlin

Publisher: Oxford University Press

Published: 2018-02-02

Total Pages: 496

ISBN-13: 0192526464

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Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptual understanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations" models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes. This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonstrations. Yet, an important goal of the book is to develop the reader's physical intuition and qualitative insights.


Ocean Wave Dynamics

Ocean Wave Dynamics

Author: Ian Young

Publisher: World Scientific

Published: 2020-03-20

Total Pages: 396

ISBN-13: 9811208689

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Ocean Wave Dynamics is the most up-to-date book of its kind on the three main processes responsible for the generation and evolution of ocean waves: (i) atmospheric input from the wind, (ii) wave breaking and (iii) nonlinear interactions.Ocean waves are important for many reasons. They are the major environmental impact on in the design of coastal or offshore structures. Ocean waves are also fundamental to the processes of coastal flooding and beach erosion. They will play a major role in storm related coastal flooding which will rise in frequency as a result of sea level rise. Ocean waves are also an important part of the coupled ocean-atmosphere system. They determine the roughness of the ocean surface and hence have an impact on winds, fluxes of energy, gases and heat to the ocean and even the stability of ice sheets.Containing the latest research on ocean waves, it is a valuable resource for an overview of knowledge in this important field.Related Link(s)


Wave Propagation in Complex Media

Wave Propagation in Complex Media

Author: George Papanicolaou

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 301

ISBN-13: 1461216788

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This IMA Volume in Mathematics and its Applications WAVE PROPAGATION IN COMPLEX MEDIA is based on the proceedings of two workshops: • Wavelets, multigrid and other fast algorithms (multipole, FFT) and their use in wave propagation and • Waves in random and other complex media. Both workshops were integral parts of the 1994-1995 IMA program on "Waves and Scattering." We would like to thank Gregory Beylkin, Robert Burridge, Ingrid Daubechies, Leonid Pastur, and George Papanicolaou for their excellent work as organizers of these meetings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO, and the Office of Naval Research (ONR), whose financial support made these workshops possible. A vner Friedman Robert Gulliver v PREFACE During the last few years the numerical techniques for the solution of elliptic problems, in potential theory for example, have been drastically improved. Several so-called fast methods have been developed which re duce the required computing time many orders of magnitude over that of classical algorithms. The new methods include multigrid, fast Fourier transforms, multi pole methods and wavelet techniques. Wavelets have re cently been developed into a very useful tool in signal processing, the solu tion of integral equation, etc. Wavelet techniques should be quite useful in many wave propagation problems, especially in inhomogeneous and nonlin ear media where special features of the solution such as singularities might be tracked efficiently.