This is the first thorough examination of weakly nonlocal solitary waves, which are just as important in applications as their classical counterparts. The book describes a class of waves that radiate away from the core of the disturbance but are nevertheless very long-lived nonlinear disturbances.
Table of ContentsPreface. Part I: Overview. 1. Introduction. Part II: Analytical Methods. 2. The Method of Multiple Scales and The epsilon-Power Series. 3. Hyperasymptotic Perturbation Theory. 4. Matched Asymptotic Expansions in the Complex Plane. 5. Stokes' Expansion, Resonance & Polycnoidal Waves. 6. Existence, Non-Existence & Symmetry. Part III: Numerical Methods. 7. Pseudospectral and Galerkin Methods. 8. Nonlinear Algebraic Equations. 9. Special Algorithms for Exponentially Small Phenomena. Part IV: Applications. 10. Water Waves: Fifth-Order Korteweg-De Vries Equation. 11. Rossby & Internal Gravity Waves: Nonlocal Higher Modes. 12. The 4 Breather. 13. Envelope Solitary Waves. 14. Separatrix Splitting & Slow Manifold. 15. Micropterons. Part V: Radiative Decay & Other Exponentially Small Phenomena. 16. Radiative Decay. 17. Non-Soliton Exponentially Small Phenomena. 18. The Future. A: Trigonometric and SECH Identities. B: SECH/TANH Series. C: Elliptic Functions. D: Solitons and Cnoidal Waves. E: Time Integration & Fourier Pseudospectral Algorithm. Glossary. References. Index.