Nonlinear ocean waves and the inverse scattering transform:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier, Acad. Press
2010
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| Ausgabe: | 1. ed. |
| Schriftenreihe: | International geophysics series
97 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVI, 917, [32] S. Ill., graph. Darst. |
| ISBN: | 9780125286299 |
Internformat
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| 100 | 1 | |a Osborne, Alfred R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear ocean waves and the inverse scattering transform |c Alfred R. Osborne |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier, Acad. Press |c 2010 | |
| 300 | |a XXVI, 917, [32] S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a International geophysics series |v 97 | |
| 650 | 4 | |a Ocean waves | |
| 650 | 4 | |a Nonlinear waves | |
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Datensatz im Suchindex
| _version_ | 1804142973738287104 |
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| adam_text | Titel: Nonlinear ocean waves and the inverse scattering transform
Autor: Osborne, Alfred R.
Jahr: 2010
Table of Contents
Preface xxiii
Part One Introduction: Nonlinear Waves 1
Chapter 1 Brief History and Overview of Nonlinear Water Waves 3
1.1 Linear and Nonlinear Fourier Analysis 3
1.2 The Nineteenth Century 6
1.2.1 Developments During the First Half of the
Nineteenth Century 6
1.2.2 The Latter Half of the Nineteenth Century 8
1.3 The Twentieth Century 10
1.4 Physically Relevant Nonlinear Wave Equations 13
1.4.1 The Korteweg-deVries Equation 13
1.4.2 The Kadomtsev-Petviashvili Equation 15
1.4.3 The Nonlinear Schrodinger Equation 17
1.4.4 Numerical Examples of Nonlinear Wave
Dynamics 23
1.5 Laboratory and Oceanographic Applications of 1ST 24
1.5.1 Laboratory Investigations 26
1.5.2 Surface Waves in the Adriatic Sea 26
1.6 Hyperfast Numerical Modeling 27
Chapter 2 Nonlinear Water Wave Equations 33
2.1 Introduction 33
2.2 Linear Equations 34
2.3 The Euler Equations 35
2.4 Wave Motion in 2 + 1 Dimensions 36
2.4.1 The Zakharov Equation 36
2.4.2 The Davey-Stewartson Equations 37
2.4.3 The Davey-Stewartson Equations in
Shallow Water 39
2.4.4 The Kadomtsev-Petviashvili Equation 39
2.4.5 The KP-Gardner Equation 40
2.4.6 The 2 + 1 Gardner Equation 40
2.4.7 The 2 + 1 Boussinesq Equation 40
Table of Contents
2.5 Wave Motion in 1 + 1 Dimensions 40
2.5.1 The Zakharov Equation 40
2.5.2 The Nonlinear Schrodinger Equation for
Arbitrary Water Depth 41
2.5.3 The Deep-Water Nonlinear Schrodinger
Equation 43
2.5.4 The KdV Equation 43
2.5.5 The KdV Equation Plus Higher-Order
Terms 43
2.6 Perspective in Terms of the Inverse Scattering
Transform 45
2.7 Characterizing Nonlinearity 46
Chapter 3 The Infinite-Line Inverse Scattering Transform 49
3.1 Introduction 49
3.2 The Fourier Transform Solution to the
Linearized KdV Equation 54
3.3 The Scattering Transform Solution to the
KdV Equation 55
3.4 The Relationship Between the Fourier Transform
and the Scattering Transform 58
3.5 Review of Assumptions Implicit in the Discrete,
Finite Fourier Transform 61
3.6 Assumptions Leading to a Discrete Algorithm for the
Direct Scattering Transform 64
Chapter 4 The Infinite-Line Hirota Method 69
4.1 Introduction 69
4.2 The Hirota Method 69
4.3 The Korteweg-deVries Equation 69
4.4 The Hirota Method for Solving the KP Equation 73
4.5 The Nonlinear Schrodinger Equation 74
4.6 The Modified KdV Equation 76
Part Two Periodic Boundary Conditions 79
Chapter 5 Periodic Boundary Conditions: Physics, Data Analysis,
Data Assimilation, and Modeling 81
5.1 Introduction 81
5.2 Riemann Theta Functions as Ordinary
Fourier Analysis 85
5.3 The Use of Generalized Fourier Series to
Solve Nonlinear Wave Equations 87
5.3.1 Near-Shore, Shallow-Water Regions 87
5.3.2 Shallow- and Deep-Water Nonlinear Wave
Dynamics for Narrow-Banded Wave Trains 89
Table of Contents
5.4 Dynamical Applications of Theta Functions 90
5.5 Data Analysis and Data Assimilation 92
5.6 Hyperfast Modeling of Nonlinear Waves 93
Chapter 6 The Periodic Hirota Method 95
6.1 Introduction 95
6.2 The Hirota Method 95
6.3 The Burgers Equation 96
6.4 The Korteweg-de Vries Equation 98
6.5 The KP Equation 100
6.6 The Nonlinear Schrodinger Equation 104
6.7 The KdV-Burgers Equation 107
6.8 The Modified KdV Equation 108
6.9 The Boussinesq Equation 108
6.10 The 2+1 Boussinesq Equation 109
6.11 The 2 + 1 Gardner Equation 109
Part Three Multidimensional Fourier Analysis 113
Chapter 7 Multidimensional Fourier Series 115
7.1 Introduction 115
7.2 Linear Fourier Series 115
7.3 Multidimensional or N-Dimensional Fourier Series 117
7.4 Conventional Multidimensional Fourier Series 118
7.5 Dynamical Multidimensional Fourier Series 120
7.6 Alternative Notations for Multidimensional Fourier
Series 122
7.6.1 Baker s Notation 123
7.6.2 Inverse Scattering Transform Notation 123
7.6.3 Relationship to Riemann Theta Functions 125
7.7 Simple Examples of Dynamical Multidimensional
Fourier Series 126
7.8 General Rules for Dealing with Dynamical
Multidimensional Fourier Series 129
7.9 Reductions of Multidimensional Fourier Series 130
7.10 Theta Functions Solve a Diffusion Equation 133
7.11 Multidimensional Fourier Series Solve Linear
Wave Equations 135
7.12 Details for Two Degrees of Freedom 138
7.13 Converting Multidimensional Fourier Series
to Ordinary Fourier Series 141
Chapter 8 Riemann Theta Functions 147
8.1 Introduction 147
8.2 Riemann Theta Functions 147
Table of Contents
8.3 Simple Properties of Theta Functions 149
8.3.1 Symmetry of the Riemann Matrix 149
8.3.2 One-Dimensional Theta Functions:
Connection to Classical Elliptic Functions 150
8.3.3 Multiple, Noninteracting Degrees of
Freedom 151
8.3.4 A Theta Function Identity 152
8.3.5 Relationship of Generalized Fourier
Series to Ordinary Fourier Series 154
8.3.6 Alternative Form for Theta Functions in
Terms of Cosines 155
8.3.7 Partial Sums of Theta Functions 157
8.3.8 Examples of Simple Partial Theta Sums 160
8.4 Statistical Properties of Theta Function Parameters 164
8.5 Theta Functions as Ordinary Fourier Series 169
8.6 Perturbation Expansion of Theta Functions in
Terms of an Interaction Parameter 173
8.7 N-Mode Interactions 175
8.8 Poisson Summation for Theta Functions 176
8.8.1 Gaussian Series for One-Degree-of-Freedom
Theta Functions 176
8.8.2 The Infinite-Line Limit 180
8.8.3 Fourier and Gaussian Series for
N-Dimensional Theta Functions 181
8.8.4 Gaussian Series for Theta Functions 182
8.8.5 One-Degree-of-Freedom Gaussian Series 182
8.8.6 Many-Degree-of-Freedom Gaussian Series 183
8.8.7 Comments on Numerical Analysis 185
8.8.8 Modular Transformations for Computing
Theta Function Parameters 185
8.9 Solitons on the Infinite Line and on the Periodic
Interval 188
8.10 N-Dimensional Theta Functions as a Sum of
One-Degree-of-Freedom Thetas 189
8.11 N-Dimensional Partial Theta Sums over
One-Degree-of-Freedom Theta Functions 191
Appendix I: Various Notations for Theta
Functions 197
Exponential Forms 197
Cosine Forms 198
Appendix II: Partial Sums of Theta Functions 199
Exponential Forms 199
Cosine Forms 199
Appendix III: Fourier Series of Theta Functions
at t = 0 200
Table of Contents
Appendix IV: Fourier Series of Theta Functions
at Time t 201
Chapter 9 Riemann Theta Functions as Ordinary Fourier Series 203
9.1 Introduction 203
9.2 Theoretical Considerations 205
9.3 A Numerical Example for the KdV Equation 208
Appendix: Theta Function Run with KP Program 215
Part Four Nonlinear Shallow-Water Spectral Theory 217
Chapter 10 The Periodic Korteweg-DeVries Equation 219
10.1 Introduction 219
10.2 Linear Fourier Series Solution to the Linearized
KdV Equation 219
10.3 The Hyperelliptic Function Solution to KdV 220
10.4 The ^-Function Solution to the KdV Equation 221
10.5 Special Cases of Solutions to the KdV Equation
to Using O-Functions 224
10.5.1 One Degree of Freedom 225
10.5.2 On the Possibility of Multiple,
Noninteracting Cnoidal Waves 230
10.5.3 The Linear Fourier Limit 231
10.5.4 The Soliton and the N-Soliton Limits 232
10.5.5 Physical Selection of the Basis Cycles 232
10.6 Exact and Approximate Solutions to the KdV
Equation for Specific Cases 233
10.6.1 A Single Cnoidal Wave 233
10.6.2 Multiple, Noninteracting Cnoidal Waves 235
10.6.3 Cnoidal Waves with Interactions 236
10.6.4 Approximate Solutions to KdV for
Partial Theta Sums 239
10.6.5 Linear Limit of KdV Solutions 242
10.6.6 Approximate Solutions to KdV for
Specific Cases 242
10.6.7 The Single Cnoidal Wave Solution to
the KdV Equation 248
10.6.8 The Ursell Number 250
10.6.9 The Cnoidal Wave as a Classical Elliptic
Function and Its Ursell Number 250
10.6.10 An Example Problem with 10 Degrees
of Freedom 253
10.6.11 Relationship of Cnoidal Wave Parameters
to the Parameter q 253
Table of Contents
10.6.12 Wave Amplitudes and Heights for Each
Degree of Freedom of KdV 255
Chapter 11 The Periodic Kadomtsev-Petviashvili Equation 261
11.1 Introduction 261
11.2 Overview of Periodic Inverse Scattering 262
11.3 Computation of the Spectral Parameters in
Terms of Schottky Uniformization 264
11.3.1 Linear Fractional Transformation 265
11.3.2 Theta Function Spectrum as Poincare
Series of Schottky Parameters 266
11.4 The Nakamura-Boyd Approach for Determining
the Riemann Spectrum 267
Part Five Nonlinear Deep-Water Spectral Theory 271
Chapter 12 The Periodic Nonlinear Schrodinger Equation 273
12.1 Introduction 273
12.2 The Nonlinear Schrodinger Equation 273
12.2.1 The Time NLS Equation and Its
Relation to Physical Experiments 274
12.2.2 A Scaled Form of the NLS Equation 275
12.2.3 Small-Amplitude Modulations of the
NLS Equation 275
12.3 Representation of the 1ST Spectrum in the
Lambda Plane 276
12.4 Overview of Modulation Theory for the NLS
Equation 278
12.5 Analytical Formulas for Unstable Wave Packets 285
12.6 Periodic Spectral Theory for the NLS Equation 288
12.6.1 The Lax Pair 288
12.6.2 The Spectra Eigenvalue Problem and
Floquet Analysis 289
12.7 Overview of the Spectrum and Hyperelliptic
Functions 293
12.7.1 The 1ST Spectrum 293
12.7.2 Generating Solutions to the NLS
Equation 295
12.7.3 Applications to the Cauchy Problem:
Space and Time Series Analysis 295
12.7.4 The Main Spectrum 296
12.7.5 The Auxiliary Spectrum of the u,(x, 0) 296
12.7.6 The Auxiliary Spectrum of the Riemann
Sheet Indices 07 297
Table of Contents
12.7.7 The Auxiliary Spectrum of the y;(x, 0) 297
Appendix-Interpretation of the Hyperelliptic
Function Superposition Law 298
Chapter 13 The Hilbert Transform 301
13.1 Introduction 301
13.2 The Hilbert Transform 304
13.2.1 Properties of the Hilbert Transform 305
13.2.2 Numerical Procedure for Determining
the Hilbert Transform 309
13.2.3 Table of Simple Hilbert Transforms 309
13.3 Narrow-Banded Processes 309
13.4 Statistical Properties of Complex Time Series 312
13.5 Relations Between the Surface Elevation and
the Complex Envelope Function 315
13.6 Fourier Representation of the Free Surface
Elevation and the Complex Envelope Function 320
13.6.1 Fourier Representations 322
13.7 Initial Modulations for Certain Special
Solutions of the NLS Equation 328
Part Six Theoretical Computation of the Riemann
Spectrum 331
Chapter 14 Algebraic-Geometric Loop Integrals 333
14.1 Introduction 333
14.2 The Theta-Function Solutions to the KdV
Equation 333
14.2.1 Holomorphic Differentials 334
14.2.2 Phases of the Theta Functions 339
14.2.3 The Period Matrix 340
14.2.4 One Degree of Freedom 341
14.2.5 Notation for Classical Jacobian Integrals 342
14.2.6 Notation for to the Theta-Function
Formulation 342
14.3 On the Possibility of Interactionless Potentials
for the Two Degree-of-Freedom Case 346
14.4 Numerical Computation of the Riemann Spectrum 348
Appendix: Summary of Formulas for the Loop
Integrals of the KdV Equation 349
Chapter 15 Schottky Uniformization 353
15.1 Introduction 353
15.2 1ST Spectral Domain 353
Table of Contents
15.3 Linear
15.3.1
15.3.2
15.3.3
15.3.4
15.3.5
15.3.6
15.3.7
15.3.8
15.3.9
Appendix I:
Appendix II:
Appendix III
Appendix IV:
Oscillation Basis 354
An Overview of Schottky Uniformization
in the Oscillation Basis 354
The Schottky Circles and Parameters 355
Linear Fractional Transformations 357
Poincare Series Relating the 1ST E-plane
to the Schottky z-plane 359
Poincare Series for the Period Matrix 360
Poincare Series for the wavenumbers and
Frequencies 361
How to Sum the Poincare Series 361
One Degree of Freedom 363
Two Degrees of Freedom 365
Schottky Uniformization in the Small-
Amplitude Limit of the Oscillation Basis 370
Compute the Images of the Floquet
Eigenvalues in the Schottky Domain 370
Compute Schottky Parameters 370
Period Matrix in Oscillatory Basis 370
Period Matrix in Soliton Basis by Modular
Transformation 370
Wavenumbers in Oscillatory Basis 371
Wavenumbers in Soliton Basis by Modular
Transformation 371
Schottky Uniformization in the
Large-Amplitude Limit of the Soliton Basis 371
Compute the Images of the Floquet
Eigenvalues in the Schottky Domain 371
Compute Schottky Parameters 371
Period Matrix in Soliton Basis 371
Period Matrix in Oscillatory Basis 372
Wavenumbers in Soliton Basis 372
Wavenumbers in Oscillatory Basis 372
: Poincare Series from the Holomorphic
Differentials 372
The Oscillation Basis of Dubrovin and
Novikov 372
The Oscillation Basis in the Schottky
Domain Due to Bobenko 375
One Degree-of-Freedom Schottky z-Plane
to 1ST E -Plane Poincare Series 377
Chapter 16 Nakamura-Boyd Approach 383
16.1 Introduction 383
16.2 The Hirota Direct Method for the KdV Equation
with Periodic Boundary Conditions 384
Table of Contents
16.3 Theta Functions with Characteristics 387
16.4 Solution of the KdV Equation for the Theta Function
with Characteristics 388
16.5 Determination of Theta-Function Parameters 390
16.6 Linearized Form for Riemann Spectrum for the KdV
Equation 392
16.7 Strategy for Determining Solutions of Nonlinear
Equations 392
16.8 One Degree-of-Freedom Riemann Spectrum
and Solution of the KdV Equation 395
16.9 Two Degrees of Freedom of Riemann Spectrum
and Solution of the KdV Equation 400
16.10 N Degrees of Freedom of Riemann Spectrum
and Solution of the KdV Equation 403
16.10.1 Form Number 1 404
16.10.2 Form Number 2 405
16.10.3 Form Number 3 406
16.11 Numerical Algorithm for Solving Nonlinear
Equations 407
16.12 Solving Systems of Two-Dimensional
Nonlinear Equations 409
Appendix: Theta Functions with Characteristics 416
Part Seven Nonlinear Numerical and Time Series
Analysis Algorithms 421
Chapter 17 Automatic Algorithm for the Spectral Eigenvalue
Problem for the KdV Equation 423
17.1 Introduction 423
17.2 Formulation of the Problem 423
17.3 Periodic 1ST for the KdV Equation in the u-Function
Representation 426
17.4 The Spectral Structure of Periodic 1ST 429
17.5 A Numerical Discretization 432
17.5.1 Formulation 432
17.5.2 Implementation of the Numerical
Algorithm 434
17.5.3 Reconstruction of Hyperelliptic
Functions and Periodic Solutions to the
KdV Equation 435
17.6 Automatic Numerical 1ST Algorithm 436
17.7 Example of the Analysis of a
Many-Degree-of-Freedom Wave Train and
Nonlinear Filtering 446
17.8 Summary and Conclusions 448
Table of Contents
Chapter 18 The Spectral Eigenvalue Problem for the NLS Equation 451
18.1 Introduction 451
18.2 Numerical Algorithm 451
18.3 The NLS Spectrum 453
18.3.1 The Main Spectrum 453
18.3.2 The Auxiliary Spectrum of the fif(x,0) 454
18.3.3 The Auxiliary Spectrum of the Riemann
Sheet Indices a, 454
18.3.4 The Auxiliary Spectrum of the y;(x,0) 454
18.3.5 Spines in the Spectrum 455
18.4 Examples of Spectral Solutions of the NLS Equation 455
18.4.1 Plane Waves 455
18.4.2 Small Modulations 455
18.5 Summary 459
Chapter 19 Computation of Algebraic-Geometric Loop Integrals
for the KdV Equation 461
19.1 Introduction 461
19.2 Convenient Transformations 461
19.2.1 First Transformation 462
19.2.2 Second Transformation 465
19.2.3 A Final Transformation 467
19.3 The Landen Transformation 468
19.4 Search for an AGM Method for the Loop Integrals 468
19.4.1 One Degree-of-Freedom Case 469
19.4.2 An Alternative Approach 471
19.4.3 Two Degree-of-Freedom Case 474
19.5 Improving Loop Integral Behavior 478
19.6 Constructing the Loop Integrals and Parameters
of Periodic 1ST 485
Chapter 20 Simple, Brute-Force Computation of Theta Functions and
Beyond 489
20.1 Introduction 489
20.2 Brute-Force Method 489
20.3 Vector Algorithm for the Theta Function 490
20.4 Theta Functions as Ordinary Fourier Series 492
20.5 A Memory-Bound Brute-Force Method 496
20.6 Poisson Series for Theta Functions 497
20.7 Decomposition of Space Series into Cnoidal
Wave Modes 497
Chapter 21 The Discrete Riemann Theta Function 501
21.1 Introduction 501
21.2 Discrete Fourier Transform 501
Table of Contents
21.3 The Multidimensional Fourier Transform 507
21.4 The Theta Function 508
21.5 The Discrete Theta Function 510
21.6 Determination of the Period Matrix and Phases
from a Space/Time Series 515
21.7 General Procedure for Computing the Period
Matrix and Phases from the Q s 521
21.8 Embedding the Discrete Theta Function 525
21.9 A Numerical Example for Extracting the Riemann
Spectrum from the Q s 526
Chapter 22 Summing Riemann Theta Functions over the N-Ellipsoid 531
22.1 Introduction 531
22.2 Summing over the N-Sphere or Hypersphere 532
22.3 The Ellipse in Two Dimensions 537
22.4 Principal Axis Coordinates in Two Dimensions 537
22.5 Solving for the Coordinate m2 in Terms of m1 541
22.6 The Case for Three and N Degrees of Freedom 543
22.7 Summation Values for mx 546
22.8 Summary of Theta-Function Summation over
Hyperellipsoid 549
22.9 Discussion of Convergence of Summation Method 552
22.10 Example Problem 553
Chapter 23 Determining the Riemann Spectrum from Data and
Simulations 557
23.1 Introduction 557
23.2 Space Series Analysis 558
23.3 Time Series Analysis 560
23.4 Nonlinear Adiabatic Annealing 561
23.5 Outline of Nonlinear Adiabatic Annealing on a
Riemann Surface 564
23.6 Establishing the Riemann Spectrum for the
Cauchy Problem 568
23.7 Data Assimilation 569
Part Eight Theoretical and Experimental Problems
in Nonlinear Wave Physics 571
Chapter 24 Nonlinear Instability Analysis of Deep-Water Wave Trains 573
24.1 Introduction 573
24.2 Unstable Modes and Their 1ST Spectra 574
24.3 Properties of Unstable Modes 578
24.4 Formulas for Unstable Modes and Breathers 583
Table of Contents
24.5 Examples of Unstable Mode (Rogue Wave)
Solutions of NLS 586
24.6 Summary and Discussion 590
Appendix Overview of Periodic Theory for the NLS
Equation with Theta Functions 591
Chapter 25 Internal Waves and Solitons 597
25.1 Introduction 597
25.2 The Andaman Sea Measurements 601
25.3 The Theory of the KdV Equation as a
Simple Nonlinear Model for Long Internal
Wave Motions 604
25.4 Background on KdV Theory and Solitons 610
25.5 Nonlinear Fourier Analysis of Soliton Wave Trains 613
25.6 Nonlinear Spectral Analysis of Andaman Sea Data 614
25.7 Extending the KdV Model to Higher Order 620
Chapter 26 Underwater Acoustic Wave Propagation 623
26.1 Introduction 623
26.2 The Parabolic Equation 625
26.3 Solving the Parabolic Equation with Fourier Series 627
26.4 Solving the Parabolic Equation Analytically 630
26.5 The Functions F(r,z) and G(r,z) as Ordinary Fourier
Series; Solution of the PE in Terms of Matrix
Equations 634
26.6 Solving the Parabolic Equation in Terms of
Multidimensional Fourier Series 638
26.7 Rewriting the Theta Functions in
Alternative Forms 640
26.8 Applying Boundary Conditions to the
Theta Functions 647
26.9 One Degree-of-Freedom Case 656
26.10 Linear Limit of the Theta-Function Formulation 657
26.11 Implementation of Multidimensional Fourier
Methods in Acoustics 659
26.12 Physical Interpretation of the Exact Solution of
the PE 663
26.13 Solving the PE for a Given Source Function 664
26.14 Range-Independent Problem 667
26.15 Determination of the Environment from
Measurements 668
26.16 Coherent Modes in the Acoustic Field 671
26.17 Shadow Zone Analysis 674
26.18 Application to Unmanned, Untethered,
Submersible Vehicles 678
Table of Contents
26.19 Application to Communications, Imaging, and
Encryption 679
Appendix: Products of Fourier Series 682
Chapter 27 Planar Vortex Dynamics 685
27.1 Introduction 685
27.2 Derivation of the Poisson Equation for Vortex
Dynamics in the Plane 688
27.3 Poisson Equation for Schrodinger Dynamics in the
Plane 691
27.4 Specific Cases of the Poisson Equation for Vortex
Dynamics in the Plane 691
27.5 Geophysical Fluid Dynamics 692
27.5.1 Linearization of the Potential Vorticity
Equation 693
27.5.2 The KdV Equation as Derived from the
Potential Vorticity Equation 694
27.6 The Poisson Equation for the Davey-Stewartson
Equations 696
27.7 Nonlinear Separation of Variables for the
Schrodinger Equation 696
27.8 Vortex Solutions of the sinh-Poisson Equation
Using Soliton Methods 698
27.9 Vortex and Wave Solutions of the sinh-Poisson
Equation Using Algebraic Geometry 701
Chapter 28 Nonlinear Fourier Analysis and Filtering of Ocean Waves 713
28.1 Introduction 713
28.2 Preliminary Considerations 714
28.3 Sine Waves and Linear Fourier Analysis 717
28.4 Cnoidal Waves and Nonlinear Fourier Analysis 718
28.5 Theoretical Background for Data Analysis
Procedures 720
28.5.1 Cnoidal Wave Decomposition Theorem
for 0-Functions 720
28.5.2 Nonlinear Filtering with 0-Functions 722
28.6 Physical Considerations and Applicability of the
Nonlinear Fourier Approach 725
28.6.1 Properties of the Nonlinear Fourier
Approach 725
28.6.2 Preliminary Tests of the Time Series 726
28.6.3 The Use of Periodic Boundary Conditions 727
28.7 Nonlinear Fourier Analysis of the Data 728
28.7.1 Applicability of the Nonlinear Fourier
Approach 729
Table of Contents
28.7.2 Analysis of the Data 730
28.7.3 Nonlinear Filtering 734
28.8 Summary and Discussion 743
Chapter 29 Laboratory Experiments of Rogue Waves 745
29.1 Introduction 745
29.2 Linear Fourier Analysis and the Nonlinear
Schrodinger Equation 747
29.3 Nonlinear Fourier Analysis for the Nonlinear
Schrodinger Equation 749
29.4 Marintek Wave Tank 750
29.5 Deterministic Wave Trains as Time Series 751
29.6 Random Wave Trains 763
29.6.1 Characteristics of Random Wave Trains
Using 1ST for NLS 763
29.6.2 Measured Random Wave Trains 767
29.6.3 Nonlinear Spectral Analysis of the
Random Wave Trains 767
29.7 Summary and Discussion 776
Chapter 30 Nonlinearity in Duck Pier Data 779
30.1 Introduction 779
30.2 The Ursell Number 780
30.2.1 Cnoidal Waves and the Spectral Ursell
Number 781
30.3 Estimates of the Ursell Number from Duck Pier
Data 785
30.4 Analysis of Duck Pier Data 787
Chapter 31 Harmonic Generation in Shallow-Water Waves 795
31.1 Introduction 795
31.2 Nonlinear Fourier Analysis 796
31.3 Nonlinear Spectral Decomposition 796
31.4 Harmonic Generation in Shallow Water 797
31.5 Periodic Inverse Scattering Theory 798
31.6 Classical Harmonic Generation and FPU
Recurrence in a Simple Model Simulation 798
31.7 Search for Harmonic Generation in
Laboratory Data 809
31.8 Summary and Discussion 815
Part Nine Nonlinear Hyperfast Numerical Modeling 819
Chapter 32 Hyperfast Modeling of Shallow-Water Waves: The KdV
and KP Equations 821
Table of Contents
32.1 Introduction 821
32.2 Overview of the Literature 822
32.3 The Inverse Scattering Transform for Periodic
Boundary Conditions 824
32.3.1 The KdV Equation 825
32.3.2 The Kadomtsev-Petviashvili Equation 827
32.4 Properties of Riemann Theta Functions and Partial
Theta Summations 831
32.4.1 The KdV Equation 831
32.4.2 The KP Equation 834
32.5 Computation of the Spectral Parameters in Terms
of Schottky Uniformization 837
32.5.1 Linear Fractional Transformation 838
32.5.2 Theta Function Spectrum as Poincare
Series of Schottky Parameters 839
32.6 Leading Order Computation of KP Spectra
Using Schottky Variables 841
32.7 The Method of Nakamura and Boyd 843
32.8 The Exact Solution of the Time Evolution of the
Fourier Components for the KP Equation 845
32.9 Numerical Procedures for Computing the Riemann
Spectrum from Poincare Series 847
32.10 Numerical Procedures for Computing the Riemann
Theta Function 848
32.11 Numerical Procedures for Computing Hyperfast
Solutions of the KP Equation 849
32.12 Numerical Example for KP Evolution 850
Chapter 33 Modeling the 2 + 1 Gardner Equation 857
33.1 Introduction 857
33.2 The 2 + 1 Gardner Equation and Its Properties 857
33.3 The Lax Pair and Hirota Bilinear Form 859
33.4 The Extended KP Equation in Physical Units 862
33.5 Physical Behavior of the Extended KP Equation 863
Chapter 34 Modeling the Davey-Stewartson (DS) Equations 867
34.1 Introduction 867
34.2 The Physical Form of the Davey-Stewartson
Equations 867
34.3 The Normalized Form of the Davey-Stewartson
Equations 870
34.4 The Hirota Bilinear Forms 872
34.4.1 Davey-Stewartson I?Surface Tension
Dominates 873
Table of Contents
34.4.2 Davey-Stewartson II-Oceanic
Waves in Shallow Water with Negligible
Surface Tension 873
34.5 Numerical Examples 874
References 877
Volumes in Series 897
Index 903
|
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| author | Osborne, Alfred R. |
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| author_role | aut |
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| author_variant | a r o ar aro |
| building | Verbundindex |
| bvnumber | BV036475513 |
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| ctrlnum | (OCoLC)750488714 (DE-599)BSZ322880882 |
| dewey-full | 551.462 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.462 |
| dewey-search | 551.462 |
| dewey-sort | 3551.462 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Physik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV036475513 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:40:17Z |
| institution | BVB |
| isbn | 9780125286299 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020347121 |
| oclc_num | 750488714 |
| open_access_boolean | |
| owner | DE-83 DE-703 |
| owner_facet | DE-83 DE-703 |
| physical | XXVI, 917, [32] S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Elsevier, Acad. Press |
| record_format | marc |
| series | International geophysics series |
| series2 | International geophysics series |
| spelling | Osborne, Alfred R. Verfasser aut Nonlinear ocean waves and the inverse scattering transform Alfred R. Osborne 1. ed. Amsterdam [u.a.] Elsevier, Acad. Press 2010 XXVI, 917, [32] S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier International geophysics series 97 Ocean waves Nonlinear waves Nichtlineare Wellengleichung (DE-588)4042104-1 gnd rswk-swf Meereswelle (DE-588)4038334-9 gnd rswk-swf Meereswelle (DE-588)4038334-9 s Nichtlineare Wellengleichung (DE-588)4042104-1 s DE-604 International geophysics series 97 (DE-604)BV000005107 97 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020347121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Osborne, Alfred R. Nonlinear ocean waves and the inverse scattering transform International geophysics series Ocean waves Nonlinear waves Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Meereswelle (DE-588)4038334-9 gnd |
| subject_GND | (DE-588)4042104-1 (DE-588)4038334-9 |
| title | Nonlinear ocean waves and the inverse scattering transform |
| title_auth | Nonlinear ocean waves and the inverse scattering transform |
| title_exact_search | Nonlinear ocean waves and the inverse scattering transform |
| title_full | Nonlinear ocean waves and the inverse scattering transform Alfred R. Osborne |
| title_fullStr | Nonlinear ocean waves and the inverse scattering transform Alfred R. Osborne |
| title_full_unstemmed | Nonlinear ocean waves and the inverse scattering transform Alfred R. Osborne |
| title_short | Nonlinear ocean waves and the inverse scattering transform |
| title_sort | nonlinear ocean waves and the inverse scattering transform |
| topic | Ocean waves Nonlinear waves Nichtlineare Wellengleichung (DE-588)4042104-1 gnd Meereswelle (DE-588)4038334-9 gnd |
| topic_facet | Ocean waves Nonlinear waves Nichtlineare Wellengleichung Meereswelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020347121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005107 |
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