موج‌های غیرخطی اقیانوس و تبدیل معکوس پراکندگی (کتاب سخت‌افزاری بین‌المللی ژئوفیزیک)

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 Content: Series Page Page ii Copyright Page Page iv Title Page II Page v Alfred R. Osborne Preface Pages xxiii-xxvi Alfred R. Osborne Part 1 - Introduction: Nonlinear Waves Review Article Pages 1-2 Alfred R. Osborne 1 - Brief History and Overview of Nonlinear Water Waves Review Article Pages 3-31 Alfred R. Osborne Chapter 2 - Nonlinear Water Wave Equations Review Article Pages 33-47 Alfred R. Osborne Chapter 3 - The Infinite-Line Inverse Scattering Transform Review Article Pages 49-68 Alfred R. Osborne Chapter 4 - The Infinite-Line Hirota Method Review Article Pages 69-77 Alfred R. Osborne Part 2 - Periodic Boundary Conditions Review Article Pages 79-80 Alfred R. Osborne Chapter 5 - Periodic Boundary Conditions: Physics, Data Analysis, Data Assimilation, and Modeling Review Article Pages 81-94 Alfred R. Osborne 6 - The Periodic Hirota Method Review Article Pages 95-111 Alfred R. Osborne Part 3 - Multidimensional Fourier Analysis Review Article Page 113 Alfred R. Osborne 7 - Multidimensional Fourier Series Review Article Pages 115-145 Alfred R. Osborne 8 - Riemann Theta Functions Review Article Pages 147-202 Alfred R. Osborne Chapter 9 - Riemann Theta Functions as Ordinary Fourier Series Review Article Pages 203-216 Alfred R. Osborne Part 4 - Nonlinear Shallow-Water Spectral Theory Review Article Page 217 Alfred R. Osborne Chapter 10 - The Periodic Korteweg-DeVries Equation Review Article Pages 219-259 Alfred R. Osborne Chapter 11 - The Periodic Kadomtsev-Petviashvili Equation Review Article Pages 261-269 Alfred R. Osborne Part 5 - Nonlinear Deep-Water Spectral Theory Review Article Page 271 Alfred R. Osborne Chapter 12 - The Periodic Nonlinear Schrödinger Equation Review Article Pages 273-299 Alfred R. Osborne 13 - The Hilbert Transform Review Article Pages 301-329 Alfred R. Osborne Part 6 - Theoretical Computation of the Riemann Spectrum Review Article Pages 331-332 Alfred R. Osborne Chapter 14 - Algebraic-Geometric Loop Integrals Review Article Pages 333-351 Alfred R. Osborne Chapter 15 - Schottky Uniformization Review Article Pages 353-382 Alfred R. Osborne Chapter 16 - Nakamura-Boyd Approach Review Article Pages 383-419 Alfred R. Osborne Part 7 - Nonlinear Numerical and Time Series Analysis Algorithms Review Article Pages 421-422 Alfred R. Osborne 17 - Automatic Algorithm for the Spectral Eigenvalue Problem for the KdV Equation Review Article Pages 423-450 Alfred R. Osborne Chapter 18 - The Spectral Eigenvalue Problem for the NLS Equation Review Article Pages 451-459 Alfred R. Osborne Chapter 19 - Computation of Algebraic-Geometric Loop Integrals for the KdV Equation Review Article Pages 461-487 Alfred R. Osborne Chapter 20 - Simple, Brute-Force Computation of Theta Functions and Beyond Review Article Pages 489-499 Alfred R. Osborne 21 - The Discrete Riemann Theta Function Review Article Pages 501-530 Alfred R. Osborne Chapter 22 - Summing Riemann Theta Functions over the N -Ellipsoid Review Article Pages 531-555 Alfred R. Osborne Chapter 23 - Determining the Riemann Spectrum from Data and Simulations Review Article Pages 557-569 Alfred R. Osborne Part 8 - Theoretical and Experimental Problems in Nonlinear Wave Physics Review Article Pages 571-572 Alfred R. Osborne 24 - Nonlinear Instability Analysis of Deep-Water Wave Trains Review Article Pages 573-595 Alfred R. Osborne Chapter 25 - Internal Waves and Solitons Review Article Pages 597-622 Alfred R. Osborne 26 - Underwater Acoustic Wave Propagation Review Article Pages 623-684 Alfred R. Osborne 27 - Planar Vortex Dynamics Review Article Pages 685-712 Alfred R. Osborne 28 - Nonlinear Fourier Analysis and Filtering of Ocean Waves Review Article Pages 713-744 Alfred R. Osborne 29 - Laboratory Experiments of Rogue Waves Review Article Pages 745-777 Alfred R. Osborne 30 - Nonlinearity in Duck Pier Data Review Article Pages 779-794 Alfred R. Osborne 31 - Harmonic Generation in Shallow-Water Waves Review Article Pages 795-817 Alfred R. Osborne Part 9 - Nonlinear Hyperfast Numerical Modeling Review Article Page 819 Alfred R. Osborne 32 - Hyperfast Modeling of Shallow-Water Waves: The KdV and KP Equations Review Article Pages 821-856 Alfred R. Osborne 33 - Modeling the 2 + 1 Gardner Equation Review Article Pages 857-866 Alfred R. Osborne 34 - Modeling the Davey-Stewartson (DS) Equations Review Article Pages 867-875 Alfred R. Osborne References Pages 877-896 International Geophysics Series Pages 897-901 Index Pages 903-917

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

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