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Nonlinear Dispersive Equations: Existence and Stability of Solitary and Periodic Travelling Wave Solutions
About this Title
Jaime Angulo Pava, IME-USP, São Paulo, Brazil
Publication: Mathematical Surveys and Monographs
Publication Year:
2009; Volume 156
ISBNs: 978-0-8218-4897-5 (print); 978-1-4704-1383-5 (online)
DOI: https://doi.org/10.1090/surv/156
MathSciNet review: MR2567568
MSC: Primary 35-02; Secondary 35B10, 35C07, 35C08, 35Q53, 37K40, 37K45
ReadershipTable of Contents
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Front/Back Matter
History, basic models, and travelling waves
- 1. Introduction and a brief review of the history
- 2. Basic models
- 3. Solitary and periodic travelling wave solutions
Well-posedness and stability definition
- 4. Introduction to part 2: well-posedness and stability definition
- 5. Initial value problem
- 6. Definition of stability
Stability theory
- 7. Introduction to part 3: stability theory
- 8. Orbital stability—the classical method
- 9. Grillakis-Shatah-Strauss’s stability approach
The Concentration-Compactness Principle in stability theory
- 10. Introduction to part 4: the concentration-compactness principle in the stability theory
- 11. Existence and stability of solitary waves for the GBO equations
- 12. More about the Concentration-Compactness Principle
- 13. Instability of solitary wave solutions
Stability of periodic travelling waves
Appendices