Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics: Generalized Solitons and Hyperasymptotic Perturbation Theory

Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics: Generalized Solitons and Hyperasymptotic Perturbation Theory

by John P. Boyd

Paperback(Softcover reprint of the original 1st ed. 1998)

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Product Details

ISBN-13: 9781461376705
Publisher: Springer US
Publication date: 10/08/2012
Series: Mathematics and Its Applications , #442
Edition description: Softcover reprint of the original 1st ed. 1998
Pages: 596
Product dimensions: 6.30(w) x 9.45(h) x 0.05(d)

Table of Contents

Preface. 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.

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