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Informationen zum Autor 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. Klappentext Bridges studies the origin of Kortewegâ¿"de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves. Zusammenfassung Nonlinear waves are pervasive in nature! but are often elusive when they are modelled and analysed. In this book the author develops a natural approach to the problem based on phase modulation. He delivers models! mechanisms! generality! universality and ease of computation! as well as developing the necessary mathematical background. Inhaltsverzeichnis 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....
