Nonlinear Ocean Waves and the Inverse Scattering Transform
(Sprache: Englisch)
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...
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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 modeling 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.
Klappentext zu „Nonlinear Ocean Waves and the Inverse Scattering Transform “
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.
Inhaltsverzeichnis zu „Nonlinear Ocean Waves and the Inverse Scattering Transform “
1. Brief History of Nonlinear Water Waves, Fourier analysis and IntegrabilityPart I: Theoretical and Physical Considerations2. Theories of Water Waves3. Introduction to Linear and Nonlinear Fourier analysis4. The Infinite-Line Inverse Scattering Transform5. The Periodic Inverse Scattering Transform6. Additional Theoretical Considerations7. Physical Perspective and Exotic Solutions8. Extending the Inverse Scattering Transform to Higher OrderPart II: Numerical and Time Series Analysis Algorithms9. Numerical Methods for Infinite-Line Boundary Conditions10. Numerical Algorithms for the Analysis of Nonlinear Space and Time Series11. Procedures for the Analysis of Nonlinear Wave Data12. Nonlinear Power Spectral AnalysisPart III: Time Series Analysis of Experimental Data13. Surface Waves in the Laboratory14. Surface Waves in the Adriatic Sea
15. Surface Waves at Duck Pier16. Surface Waves in the North Sea17. Internal Waves in the Andaman SeaPart IV: Future Directions18. Engineering Applications of IST19. Chaotic Dynamics Nonlinear Wave Equations and Water Waves
Autoren-Porträt von Alfred R. Osborne
Alfred Osborne
Bibliographische Angaben
- Autor: Alfred R. Osborne
- 2010, 917 Seiten, Maße: 15,5 x 23,1 cm, Gebunden, Englisch
- Verlag: Academic Press
- ISBN-10: 0125286295
- ISBN-13: 9780125286299
Sprache:
Englisch
Rezension zu „Nonlinear Ocean Waves and the Inverse Scattering Transform “
"The book is an encyclopaedia of mathematical models of nonlinear ocean waves and methods of their investigation."--Zentralblatt MATH 1250 "The book should be of great interest not only to oceanographers, but to others interested in the intriguing physics of nonlinear waves. Much of the theory developed in the book applies to other branches of physics, such as plasma physics and nonlinear optics. Because of the high quality of writing, this book may make an ideal focus for graduate-level seminars as well as being a comprehensive reference text on nonlinear water waves."--Pure and Applied Geophysics
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