Nonlinear Ocean Waves and the Inverse Scattering Transform Book

Nonlinear Ocean Waves and the Inverse Scattering Transform


  • Author : Alfred R. Osborne
  • Publisher : Unknown
  • Release Date : 2010
  • Genre: Science
  • Pages : 917
  • ISBN 10 : 0125286295
  • Total Read : 86
  • File Size : 8,9 Mb

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Nonlinear Ocean Waves and the Inverse Scattering Transform 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 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

Scattering  Two Volume Set Book

Scattering Two Volume Set


  • Author : E. R. Pike
  • Publisher : Academic Press
  • Release Date : 2002
  • Genre: Mathematics
  • Pages : 985
  • ISBN 10 : 9780126137606
  • Total Read : 71
  • File Size : 12,6 Mb

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Scattering Two Volume Set 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 -- Scattering in Oceans -- Part 2: SCATTERING IN MICROSCOPIC PHYSICS AND CHEMICAL PHYSICS -- Introduction to direct potential scattering -- Introduction to Inverse Potential Scattering -- Visible and Near-visible Light Scattering -- Practical Aspects of Visible and Near-visible Light Scattering -- Nonlinear Light Scattering -- Atomic and Molecular Scattering: Introduction to Scattering in Chemical -- X-ray Scattering -- Neutron Scattering -- Electron Diffraction and Scattering -- Part 3: SCATTERING IN NUCLEAR PHYSICS -- Nuclear Physics -- Part 4: PARTICLE SCATTERING -- State of the Art of Peturbative Methods -- Scattering Through Electro-weak Interactions (the Fermi Scale) -- Scattering Through Strong Interactions (the Hadronic or QCD Scale) -- Part 5: SCATTERING AT EXTREME PHYSICAL SCALES -- Scattering at Extreme Physical Scales -- Part 6: SCATTERING IN MATHEMATICS AND NON-PHYSICAL SCIENCES -- Relations with Other Mathematical Theories -- Inverse Scattering Transform and Non-linear Partial Differenttial Equations -- Scattering of Mathematical Objects.

Nonlinear Ocean Waves and the Inverse Scattering Transform Book

Nonlinear Ocean Waves and the Inverse Scattering Transform


  • Author : Alfred Osborne
  • Publisher : Academic Press
  • Release Date : 2010-04-07
  • Genre: Science
  • Pages : 944
  • ISBN 10 : 0080925103
  • Total Read : 96
  • File Size : 7,9 Mb

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Nonlinear Ocean Waves and the Inverse Scattering Transform 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 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

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations Book

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations


  • Author : Pham Loi Vu
  • Publisher : CRC Press
  • Release Date : 2019-11-11
  • Genre: Mathematics
  • Pages : 388
  • ISBN 10 : 9781000708684
  • Total Read : 97
  • File Size : 11,7 Mb

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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations 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 physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features • The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. • Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. • The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. • Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.

Guided Wave Optics Book

Guided Wave Optics


  • Author : Boris Malomed
  • Publisher : MDPI
  • Release Date : 2018-03-23
  • Genre: Electronic books
  • Pages : 323
  • ISBN 10 : 9783038426141
  • Total Read : 62
  • File Size : 10,8 Mb

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Guided Wave Optics Summary:

This book is a printed edition of the Special Issue "Guided-Wave Optics" that was published in Applied Sciences

Princeton Companion to Applied Mathematics Book

Princeton Companion to Applied Mathematics


  • Author : Nicholas J. Higham
  • Publisher : Princeton University Press
  • Release Date : 2015-09-09
  • Genre: Mathematics
  • Pages : 1014
  • ISBN 10 : 9780691150390
  • Total Read : 94
  • File Size : 18,9 Mb

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Princeton Companion to Applied Mathematics Summary:

The must-have compendium on applied mathematics 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; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Dynamics of the Equatorial Ocean Book

Dynamics of the Equatorial Ocean


  • Author : John P. Boyd
  • Publisher : Springer
  • Release Date : 2017-09-25
  • Genre: Science
  • Pages : 517
  • ISBN 10 : 9783662554760
  • Total Read : 74
  • File Size : 20,9 Mb

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Dynamics of the Equatorial Ocean 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 jet model, generation of coastal Kelvin waves from equatorial waves by reflection, Rossby solitary waves, and Kelvin frontogenesis. A series of appendices on midlatitude theories for waves, jets and wave reflections add further material to assist the reader in understanding the differences between the same phenomenon in the equatorial zone versus higher latitudes.

Nonlinear Ocean Dynamics Book

Nonlinear Ocean Dynamics


  • Author : Maged Marghany
  • Publisher : Elsevier
  • Release Date : 2021-02-09
  • Genre: Science
  • Pages : 462
  • ISBN 10 : 9780128209257
  • Total Read : 64
  • File Size : 6,7 Mb

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Nonlinear Ocean Dynamics Summary:

Nonlinear Ocean Dynamics: Synthetic Aperture Radar delivers the critical tools needed to understand the latest technology surrounding the radar imaging of nonlinear waves, particularly microwave radar, as a main source to understand, analyze and apply concepts in the field of ocean dynamic surface. Filling the gap between modern physics quantum theory and applications of radar imaging of ocean dynamic surface, this reference is packed with technical details associated with the potentiality of synthetic aperture radar (SAR). The book also includes key methods needed to extract the value-added information necessary, such as wave spectra energy, current pattern velocity, internal waves, and more. This book also reveals novel speculation of a shallow coastal front: named as Quantized Marghany's Front. Rounding out with practical simulations of 4-D wave-current interaction patterns using using radar images, the book brings an effective new source of technology and applications for today’s coastal scientists and engineers. Solves specific problems surrounding the nonlinearity of ocean surface dynamics in synthetic aperture radar data Helps develop new algorithms for retrieving ocean wave spectra and ocean current movements from synthetic aperture radar Includes over 100 equations that illustrate how to follow examples in the book