Weakly Nonlocal Solitary Waves and Beyond-All-Orders Asymptotics

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

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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.
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Product details

  • Hardback | 596 pages
  • 160 x 241.3 x 40.6mm | 975.23g
  • Dordrecht, Netherlands
  • English
  • 1998 ed.
  • XIX, 596 p.
  • 0792350723
  • 9780792350729

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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