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- Nonlinear Ocean Waves and the Inverse Scattering Transform

- Author : Alfred R. Osborne
- Publsiher : Unknown
- Release : 24 July 2021
- ISBN : 9780125286299
- Pages : 917 pages
- Rating : /5 from reviews

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Download or read book entitled *Nonlinear Ocean Waves and the Inverse Scattering Transform* by author: *Alfred R. Osborne* which was release on *24 July 2021* and published by *Unknown* with total page 917 pages . This book available in PDF, EPUB and Kindle Format. 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

- Author : Alfred R. Osborne
- Publisher : Unknown
- Release Date : 2010
- Total pages : 917
- ISBN : 9780125286299

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**Summary :** 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 ...

- Author : Alfred Osborne
- Publisher : Academic Press
- Release Date : 2010-04-07
- Total pages : 944
- ISBN : 9780125286299

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**Summary :** 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 ...

- Author : E. R. Pike,Pierre C. Sabatier
- Publisher : Academic Press
- Release Date : 2002
- Total pages : 1831
- ISBN : 9780125286299

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**Summary :** Part 1: SCATTERING OF WAVES BY MACROSCOPIC TARGET -- Interdisciplinary aspects of wave scattering -- Acoustic scattering -- Acoustic scattering: approximate methods -- Electromagnetic wave scattering: theory -- Electromagnetic wave scattering: approximate and numerical methods -- Electromagnetic wave scattering: applications -- Elastodynamic wave scattering: theory -- Elastodynamic wave scattering: Applications -- ...

- Author : A. R. Osborne,HAWAII UNIV HONOLULU DEPT OF OCEANOGRAPHY.
- Publisher : Unknown
- Release Date : 1993
- Total pages : 23
- ISBN : 9780125286299

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**Summary :** Nonlinear Fourier analysis is discussed as it arises from the exact spectral solution to large classes of nonlinear wave equations which are integrable by the inverse scattering transform (IST). The approach may be viewed as a generalization of the ordinary, linear Fourier transform or Fourier series. Numerical methods are discussed ...

- Author : Harvey Segur
- Publisher : Unknown
- Release Date : 1980
- Total pages : 71
- ISBN : 9780125286299

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**Summary :** Under appropriate conditions, ocean waves may be modeled by certain nonlinear evolution equations that admit soliton solutions and can be solved exactly by the inverse scattering transform (IST). The theory of these special equations is developed in five lectures. As physical models, these equations typically govern the evolution of narrow-band ...

- Author : Pham Loi Vu
- Publisher : CRC Press
- Release Date : 2019-11-11
- Total pages : 388
- ISBN : 9780125286299

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**Summary :** Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical ...

- Author : Miguel Onorato,Stefania Resitori,Fabio Baronio
- Publisher : Springer
- Release Date : 2016-09-19
- Total pages : 370
- ISBN : 9780125286299

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**Summary :** 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 ...

- Author : Nicholas J. Higham
- Publisher : Princeton University Press
- Release Date : 2015-09-15
- Total pages : 1016
- ISBN : 9780125286299

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**Summary :** This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; ...

- Author : John P. Boyd
- Publisher : Springer
- Release Date : 2017-09-25
- Total pages : 517
- ISBN : 9780125286299

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**Summary :** This book is the first comprehensive introduction to the theory of equatorially-confined waves and currents in the ocean. Among the topics treated are inertial and shear instabilities, wave generation by coastal reflection, semiannual and annual cycles in the tropic sea, transient equatorial waves, vertically-propagating beams, equatorial Ekman layers, the Yoshida ...

- Author : Kuppuswamy Porsezian,Ramanathan Ganapathy
- Publisher : CRC Press
- Release Date : 2017-12-19
- Total pages : 568
- ISBN : 9780125286299

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**Summary :** Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications presents a collection of breakthrough research portraying the odyssey of light from optical solitons to optical rogue waves in nonlinear optical fibers. The book provides a simple yet holistic view on the theoretical and application-oriented aspects of light, with a ...

- Author : Dmitry V. Chalikov
- Publisher : Springer
- Release Date : 2016-06-25
- Total pages : 330
- ISBN : 9780125286299

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**Summary :** Presenting a novel approach to wave theory, this book applies mathematical modeling to the investigation of sea waves. It presents problems, solutions and methods, and explores issues such as statistical properties of sea waves, generation of turbulence, Benjamin-Feir instability and the development of wave fields under the action of wind. ...

- Author : Yiu-Chung Hon,Masahiro Yamamoto
- Publisher : World Scientific
- Release Date : 2003
- Total pages : 454
- ISBN : 9780125286299

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**Summary :** Annotation. Proceedings from the First International Conference on Inverse Problems, Recent Theoretical Development and Numerical Approaches, held at the City University of Hong Kong from January 9-12, 2002....

- Author : Elena Tobisch
- Publisher : Springer
- Release Date : 2015-08-19
- Total pages : 298
- ISBN : 9780125286299

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**Summary :** 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 (...

- Author : Thomas J. Bridges
- Publisher : Cambridge University Press
- Release Date : 2017-07-03
- Total pages : 212
- ISBN : 9780125286299

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**Summary :** Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of ...

- Author : Mark J. Ablowitz,Harvey Segur
- Publisher : SIAM
- Release Date : 2006-05-15
- Total pages : 425
- ISBN : 9780125286299

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**Summary :** A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised ...