Nonlinear Ocean Waves & amp; the Inverse Scattering Transform

For more than 200 years, the Fourier Transformation of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering . Quantcast for Rossie 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 linear Generalization of Fourier analysis Referred it as the inverse scattering transform, the fundamental building block of Which is a generalized Fourier series called the Riemann theta function. Elucidating the art of science and research in the context of the book.

• presents techniques and methods of the scattering transform for data analysis






• geared toward both mathematical and numerical analysis








• suitable for classroom teaching as well as research

Contents

Preface

1. Brief History of Nonlinear Water Waves, Fourier analysis and Integrability

Part I: Theoretical and Physical Considerations

2. Theories of Water Waves

3. Introduction to Linear and Nonlinear Fourier analysis

4. The Infinite-Line Inverse Scattering Transform

5. The Periodic Inverse Scattering Transform

6. Additional Theoretical Considerations

7. Physical Perspective and Exotic Solutions

8. Extending the Inverse Scattering Transform to Higher Order

Part II: Numerical and Time Series Analysis Algorithms

9. Numerical Methods for Infinite-Line Boundary Conditions

10. Numerical Algorithms for the Analysis of Nonlinear Space and Time Series

11. Procedures for the Analysis of Nonlinear Wave Data

12. Nonlinear Power Spectral Analysis

Part II: Time Series. Analysis of Experimental Data

13. Surface Waves in the Laboratory

14. Surface Waves in the Adriatic Sea

15. Surface Waves at Duck Pier

16. Surface Waves in the North Sea

17. Internal Waves in the Andaman Sea

Part IV: Future Directions

18. Engineering Applications of IST

19. Chaotic Dynamics Nonlinear Wave Equations and Water Waves