Thomas J. Bridges is currently Professor of Mathematics at the University of Surrey. He has been researching the theory of nonlinear waves for over 25 years. He is co-editor of the volume Lectures on the Theory of Water Waves (Cambridge, 2016) and he has over 140 published papers on such diverse topics as multisymplectic structures, Hamiltonian dynamics, ocean wave energy harvesting, geometric numerical integration, stability of nonlinear waves, the geometry of the Hopf bundle, theory of water waves and phase modulation.
Inhaltsangabe
1. Introduction 2. Hamiltonian ODEs and relative equilibria 3. Modulation of relative equilibria 4. Revised modulation near a singularity 5. Introduction to Whitham Modulation Theory - the Lagrangian viewpoint 6. From Lagrangians to Multisymplectic PDEs 7. Whitham Modulation Theory - the multisymplectic viewpoint 8. Phase modulation and the KdV equation 9. Classical view of KdV in shallow water 10. Phase modulation of uniform flows and KdV 11. Generic Whitham Modulation Theory in 2+1 12. Phase modulation in 2+1 and the KP equation 13. Shallow water hydrodynamics and KP 14. Modulation of three-dimensional water waves 15. Modulation and planforms 16. Validity of Lagrangian-based modulation equations 17. Non-conservative PDEs and modulation 18. Phase modulation - extensions and generalizations Appendix A. Supporting calculations - 4th and 5th order terms Appendix B. Derivatives of a family of relative equilibria Appendix C. Bk and the spectral problem Appendix D. Reducing dispersive conservation laws to KdV Appendix E. Advanced topics in multisymplecticity References Index.
1. Introduction 2. Hamiltonian ODEs and relative equilibria 3. Modulation of relative equilibria 4. Revised modulation near a singularity 5. Introduction to Whitham Modulation Theory - the Lagrangian viewpoint 6. From Lagrangians to Multisymplectic PDEs 7. Whitham Modulation Theory - the multisymplectic viewpoint 8. Phase modulation and the KdV equation 9. Classical view of KdV in shallow water 10. Phase modulation of uniform flows and KdV 11. Generic Whitham Modulation Theory in 2+1 12. Phase modulation in 2+1 and the KP equation 13. Shallow water hydrodynamics and KP 14. Modulation of three-dimensional water waves 15. Modulation and planforms 16. Validity of Lagrangian-based modulation equations 17. Non-conservative PDEs and modulation 18. Phase modulation - extensions and generalizations Appendix A. Supporting calculations - 4th and 5th order terms Appendix B. Derivatives of a family of relative equilibria Appendix C. Bk and the spectral problem Appendix D. Reducing dispersive conservation laws to KdV Appendix E. Advanced topics in multisymplecticity References Index.
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