Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics Generalized Solitons and Hyperasymptotic Perturbation Theory
" . . . if a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations. " - T. Maxworthy (1980), pg. 52. The discover of nonlocal solitary waves is unknown and anonymous, but he or she lived in the dry north of Aus...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer US
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Mathematics and Its Applications
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Overview
- 1 Introduction
- II Analytical Methods
- 2 The Method of Multiple Scales and the E-Power Series
- 3 Hyperasymptotic Perturbation Theory
- 4 Matched Asymptotic Expansions in The Complex Plane
- 5 Stokes’ Expansion, Resonance & Polycnoidal Waves
- 6 Theorems and Proofs: Existence Non-Existence & Symmetry
- III Numerical Methods
- 7 Pseudospectral and Galerkin Methods
- 8 Nonlinear Algebraic Equations
- 9 Special Algorithms for Exponentially Small Phenomena
- IV Applications
- 10 Water Waves: Fifth-Order Korteweg-Devries Equation
- 11 Rossby & Internal Gravity Waves: Nonlocal Higher Modes
- 12 The ?4 Breather
- 13 Envelope Solitary Waves: Third Order Nonlinear Schroedinger Equation and the Klein-Gordon Equation
- 14 Temporal Analogues: Separatrix Splitting &The Slow Manifold
- 15 Micropterons
- V Radiative Decay &Other Exponentially Small Phenomena
- 16 Radiative Decay Of Weakly Nonlocal Solitary Waves
- 17 Non-Soliton Exponentially Small Phenomena
- 18 The Future
- References