Nonlinear Random Waves
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Nonlinear Random Waves
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Author : Vladimir V. Konotop
language : en
Publisher: World Scientific
Release Date : 1994
Nonlinear Random Waves written by Vladimir V. Konotop and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
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
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Author : Vladimir V Konotop
language : en
Publisher: World Scientific
Release Date : 1994-07-26
Nonlinear Random Waves written by Vladimir V Konotop and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-26 with Science categories.
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 And Turbulence In Nondispersive Media
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Author : S. N. Gurbatov
language : ru
Publisher: John Wiley & Sons
Release Date : 1992-03-01
Nonlinear Random Waves And Turbulence In Nondispersive Media written by S. N. Gurbatov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-01 with categories.
This book is a theoretical study of the evolution laws of random nonlinear waves of diverse physical nature propagating in nondispersive media. The book discusses the experience gained when developing an approach mainly relying on a body of Lagrangian and Eulerian statistics of random fields. This method aims to allow one to embrace in a unified manner a wide variety of random strongly nonlinear waves in nondispersive media, to reveal their specific features and fundamental evolution laws, and, finally, to apply the results to the solution of some particular physical problems.
New Approaches To Nonlinear Waves
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Author : Elena Tobisch
language : en
Publisher: Springer
Release Date : 2015-08-19
New Approaches To Nonlinear Waves written by Elena Tobisch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Science categories.
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the applicability of these novel methods and approaches to a wide class of evolutionary dispersive PDEs, e.g. equations from Benjamin-Oro, Boussinesq, Hasegawa-Mima, KdV-type, Klein-Gordon, NLS-type, Serre, Shamel , Whitham and Zakharov. This makes the book interesting for professionals in the fields of nonlinear physics, applied mathematics and fluid mechanics as well as students who are studying these subjects. The book can also be used as a basis for a one-semester lecture course in applied mathematics or mathematical physics.
Nonlinear Water Waves
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Author : David Henry
language : en
Publisher: Springer Nature
Release Date : 2019-11-27
Nonlinear Water Waves written by David Henry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-27 with Mathematics categories.
The motion of water is governed by a set of mathematical equations which are extremely complicated and intractable. This is not surprising when one considers the highly diverse and intricate physical phenomena which may be exhibited by a given body of water. Recent mathematical advances have enabled researchers to make major progress in this field, reflected in the topics featured in this volume. Cutting-edge techniques and tools from mathematical analysis have generated strong rigorous results concerning the qualitative and quantitative physical properties of solutions of the governing equations. Furthermore, accurate numerical computations of fully-nonlinear steady and unsteady water waves in two and three dimensions have contributed to the discovery of new types of waves. Model equations have been derived in the long-wave and modulational regime using Hamiltonian formulations and solved numerically. This book brings together interdisciplinary researchers working in the field of nonlinear water waves, whose contributions range from survey articles to new research results which address a variety of aspects in nonlinear water waves. It is motivated by a workshop which was organised at the Erwin Schrödinger International Institute for Mathematics and Physics in Vienna, November 27-December 7, 2017. The key aim of the workshop was to describe, and foster, new approaches to research in this field. This is reflected in the contents of this book, which is aimed to stimulate both experienced researchers and students alike.
Nonlinear Ocean Waves And The Inverse Scattering Transform
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Author : Alfred Osborne
language : en
Publisher: Academic Press
Release Date : 2010-04-07
Nonlinear Ocean Waves And The Inverse Scattering Transform written by Alfred Osborne and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-07 with Science categories.
For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface and internal waves. Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function. Elucidating the art and science of implementing these functions in the context of physical and time series analysis is the goal of this book. - Presents techniques and methods of the inverse scattering transform for data analysis - Geared toward both the introductory and advanced reader venturing further into mathematical and numerical analysis - Suitable for classroom teaching as well as research
Rogue And Shock Waves In Nonlinear Dispersive Media
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Author : Miguel Onorato
language : en
Publisher: Springer
Release Date : 2016-09-19
Rogue And Shock Waves In Nonlinear Dispersive Media written by Miguel Onorato and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Science categories.
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.
Wave Turbulence
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Author : Sergey Nazarenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-12
Wave Turbulence written by Sergey Nazarenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-12 with Science categories.
Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
Introduction To The Mathematical Physics Of Nonlinear Waves
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Author : Minoru Fujimoto
language : zh-CN
Publisher:
Release Date : 2021
Introduction To The Mathematical Physics Of Nonlinear Waves written by Minoru Fujimoto and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematical physics categories.
Nonlinear Random Waves In A Dispersive Medium
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Author : Alan C. Newell
language : en
Publisher:
Release Date : 1965
Nonlinear Random Waves In A Dispersive Medium written by Alan C. Newell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.