Thomas J Bridges
Symmetry, Phase Modulation and Nonlinear Waves
Thomas J Bridges
Symmetry, Phase Modulation and Nonlinear Waves
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Bridges studies the origin of Kortewegâ¿"de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
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Bridges studies the origin of Kortewegâ¿"de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.
Produktdetails
- Produktdetails
- Verlag: Cambridge University Press
- Seitenzahl: 236
- Erscheinungstermin: 3. Juli 2017
- Englisch
- Abmessung: 236mm x 154mm x 20mm
- Gewicht: 465g
- ISBN-13: 9781107188846
- ISBN-10: 1107188849
- Artikelnr.: 48415951
- Verlag: Cambridge University Press
- Seitenzahl: 236
- Erscheinungstermin: 3. Juli 2017
- Englisch
- Abmessung: 236mm x 154mm x 20mm
- Gewicht: 465g
- ISBN-13: 9781107188846
- ISBN-10: 1107188849
- Artikelnr.: 48415951
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.
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.
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.
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.