Symmetry, Phase Modulation and Nonlinear Waves

ISBN-13: 9781107188846 / Angielski / Twarda / 2017 / 236 str.

Thomas J. Bridges

Opis

Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.

Recenzje

'The book is clearly written, and only the most basic knowledge of Hamiltonian and Lagrangian theories is required.' Wen-Xiu Ma, MathSciNet

Spis treści

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.