Symmetry, Phase Modulation and Nonlinear Waves
eBook - PDF

Symmetry, Phase Modulation and Nonlinear Waves

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

Symmetry, Phase Modulation and Nonlinear Waves

About this book

Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

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Yes, you can access Symmetry, Phase Modulation and Nonlinear Waves by Thomas J. Bridges in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Fluid Mechanics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title page
  3. Series page
  4. Title page
  5. Copyright page
  6. Dedication
  7. Contents
  8. 1 Introduction
  9. 2 Hamiltonian ODEs and Relative Equilibria
  10. 3 Modulation of Relative Equilibria
  11. 4 Revised Modulation Near a Singularity
  12. 5 Whitham Modulation Theory – the Lagrangian Viewpoint
  13. 6 From Lagrangians to Multisymplectic PDEs
  14. 7 Whitham Modulation Theory – the Multisymplectic Viewpoint
  15. 8 Phase Modulation and the KdV Equation
  16. 9 Classical View of KdV in Shallow Water
  17. 10 Phase Modulation of Uniform Flows and KdV
  18. 11 Generic Whitham Modulation Theory in 2+1
  19. 12 Phase Modulation in 2+1 and the KP Equation
  20. 13 Shallow Water Hydrodynamics and KP
  21. 14 Modulation of Three-Dimensional Water Waves
  22. 15 Modulation and Planforms
  23. 16 Validity of Lagrangian-based Modulation Equations
  24. 17 Non-conservative PDEs and Modulation
  25. 18 Phase Modulation: Extensions and Generalizations
  26. Appendix A Supporting Calculations: Fourth- and Fifth-Order Terms
  27. Appendix B Derivatives of a Family of Relative Equilibria
  28. Appendix C B[sub(k)] and the Spectral Problem
  29. Appendix D Reducing Dispersive Conservation Laws to KdV
  30. Appendix E Advanced Topics in Multisymplecticity
  31. References
  32. Index