Physics of Nonlinear Waves
eBook - PDF

Physics of Nonlinear Waves

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Physics of Nonlinear Waves

About this book

This is an introductory book about nonlinear waves. It focuses on two properties that various different wave phenomena have in common, the "nonlinearity" and "dispersion", and explains them in a style that is easy to understand for first-time students.

Both of these properties have important effects on wave phenomena. Nonlinearity, for example, makes the wave lean forward and leads to wave breaking, or enables waves with different wavenumber and frequency to interact with each other and exchange their energies.

Dispersion, for example, sorts irregular waves containing various wavelengths into gentler wavetrains with almost uniform wavelengths as they propagate, or cause a difference between the propagation speeds of the wave waveform and the wave energy.

Many phenomena are introduced and explained using water waves as an example, but this is just a tool to make it easier to draw physical images. Most of the phenomena introduced in this book are common to all nonlinear and dispersive waves.

This book focuses on understanding the physical aspects of wave phenomena, and requires very little mathematical knowledge. The necessary minimum knowledges about Fourier analysis, perturbation method, dimensional analysis, the governing equations of water waves, etc. are provided in the text and appendices, so even second- or third-year undergraduate students will be able to fully understand the contents of the book and enjoy the fan of nonlinear wave phenomena without relying on other books.

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Yes, you can access Physics of Nonlinear Waves by Mitsuhiro Tanaka in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Copyright page
  3. Title page
  4. Contents
  5. Preface
  6. Acknowledgments
  7. The Simplest Nonlinear Wave Equation
  8. Burgers Equation: Effect of Diffusion
  9. Basics of Linear Water Waves
  10. Perturbation Method and Multiple Scale Analysis
  11. KdV Equation: Effect of Dispersion
  12. Modulation and Self-Interaction of a Wavetrain
  13. Resonant Interaction Between Waves
  14. Wave Turbulence: Interaction of Innumerable Waves
  15. Conservation Law in 3D
  16. System of Simultaneous Wave
  17. Summary of Fourier Analysis
  18. Derivation of Governing
  19. Summary to Dimensional
  20. Derivation of the KdV
  21. FPU Recurrence and the KdV
  22. Author’s Biography
  23. Index