Nonlinear Ocean Waves and the Inverse Scattering Transform

Nonlinear Ocean Waves and the Inverse Scattering Transform

Author: Alfred Osborne

Publisher: Academic Press

Published: 2010-04-07

Total Pages: 977

ISBN-13: 0080925103

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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


Book Synopsis Nonlinear Ocean Waves and the Inverse Scattering Transform by : Alfred Osborne

Download or read book Nonlinear Ocean Waves and the Inverse Scattering Transform written by Alfred Osborne and published by Academic Press. This book was released on 2010-04-07 with total page 977 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Scattering, Two-Volume Set

Author: E. R. Pike

Publisher: Academic Press

Published: 2002

Total Pages: 985

ISBN-13: 0126137609

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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.


Book Synopsis Scattering, Two-Volume Set by : E. R. Pike

Download or read book Scattering, Two-Volume Set written by E. R. Pike and published by Academic Press. This book was released on 2002 with total page 985 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Waves And Inverse Scattering Transform

Nonlinear Waves And Inverse Scattering Transform

Author: Spencer P Kuo

Publisher: World Scientific

Published: 2023-06-26

Total Pages: 198

ISBN-13: 1800614055

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Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations (NLPDEs). This book was prepared to familiarize students with nonlinear waves and methods of solving NLPDEs, which will enable them to expand their studies into related areas. The selection of topics and the focus given to each provide essential materials for a lecturer teaching a nonlinear wave course.Chapter 1 introduces 'mode' types in nonlinear systems as well as Bäcklund transform, an indispensable technique to solve generic NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST), addressing the initial value problems of a group of NLPDEs. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps for applying IST to solve NLPDEs for solitary solutions are illustrated in Chapter 6.


Book Synopsis Nonlinear Waves And Inverse Scattering Transform by : Spencer P Kuo

Download or read book Nonlinear Waves And Inverse Scattering Transform written by Spencer P Kuo and published by World Scientific. This book was released on 2023-06-26 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations (NLPDEs). This book was prepared to familiarize students with nonlinear waves and methods of solving NLPDEs, which will enable them to expand their studies into related areas. The selection of topics and the focus given to each provide essential materials for a lecturer teaching a nonlinear wave course.Chapter 1 introduces 'mode' types in nonlinear systems as well as Bäcklund transform, an indispensable technique to solve generic NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST), addressing the initial value problems of a group of NLPDEs. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps for applying IST to solve NLPDEs for solitary solutions are illustrated in Chapter 6.

Nonlinear Waves

Nonlinear Waves

Author: Lokenath Debnath

Publisher: CUP Archive

Published: 1983-12-30

Total Pages: 376

ISBN-13: 9780521254687

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The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.


Book Synopsis Nonlinear Waves by : Lokenath Debnath

Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

Nonlinear Waves

Nonlinear Waves

Author: Lokenath Debnath

Publisher: Cambridge University Press

Published: 2009-01-08

Total Pages: 372

ISBN-13: 0511868618

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The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.


Book Synopsis Nonlinear Waves by : Lokenath Debnath

Download or read book Nonlinear Waves written by Lokenath Debnath and published by Cambridge University Press. This book was released on 2009-01-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.

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: 370

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.


Book Synopsis Rogue and Shock Waves in Nonlinear Dispersive Media by : Miguel Onorato

Download or read book Rogue and Shock Waves in Nonlinear Dispersive Media written by Miguel Onorato and published by Springer. This book was released on 2016-09-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Guided-Wave Optics

Guided-Wave Optics

Author: Boris Malomed

Publisher: MDPI

Published: 2018-03-23

Total Pages: 323

ISBN-13: 3038426148

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


Book Synopsis Guided-Wave Optics by : Boris Malomed

Download or read book Guided-Wave Optics written by Boris Malomed and published by MDPI. This book was released on 2018-03-23 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Guided-Wave Optics" that was published in Applied Sciences

Nonlinear Waves in Integrable and Nonintegrable Systems

Nonlinear Waves in Integrable and Nonintegrable Systems

Author: Jianke Yang

Publisher: SIAM

Published: 2010-01-01

Total Pages: 453

ISBN-13: 0898719682

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Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.


Book Synopsis Nonlinear Waves in Integrable and Nonintegrable Systems by : Jianke Yang

Download or read book Nonlinear Waves in Integrable and Nonintegrable Systems written by Jianke Yang and published by SIAM. This book was released on 2010-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind.

The Princeton Companion to Applied Mathematics

The Princeton Companion to Applied Mathematics

Author: Nicholas J. Higham

Publisher: Princeton University Press

Published: 2015-09-15

Total Pages: 1016

ISBN-13: 1400874475

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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


Book Synopsis The Princeton Companion to Applied Mathematics by : Nicholas J. Higham

Download or read book The Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-15 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Nonlinear Dynamics Of Ocean Waves - Proceedings Of The Symposium

Nonlinear Dynamics Of Ocean Waves - Proceedings Of The Symposium

Author: Michael F Shlesinger

Publisher: World Scientific

Published: 1992-08-31

Total Pages: 230

ISBN-13: 9814554529

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The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.


Book Synopsis Nonlinear Dynamics Of Ocean Waves - Proceedings Of The Symposium by : Michael F Shlesinger

Download or read book Nonlinear Dynamics Of Ocean Waves - Proceedings Of The Symposium written by Michael F Shlesinger and published by World Scientific. This book was released on 1992-08-31 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for “new physics”. The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space — an arena of events treated in the Standard Model as a classical background — is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This book discusses an extension of this view by replacing space with phase space. It combines the results of the author's research papers and places them in much broader philosophical and phenomenological contexts, thus providing further arguments in favor of the proposed alternative. The book should be of interest to the philosophically-minded readers who are willing to contemplate unorthodox ideas on the very nature of the world.