**Contemporary Mathematics**

Volume: 200;
1996;
235 pp;
Softcover

MSC: Primary 76; 35;

Print ISBN: 978-0-8218-0510-7

Product Code: CONM/200

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

**Electronic ISBN: 978-0-8218-7791-3
Product Code: CONM/200.E**

List Price: $71.00

AMS Member Price: $56.80

MAA Member Price: $63.90

# Mathematical Problems in the Theory of Water Waves

Share this page *Edited by *
*F. Dias; J.-M. Ghidaglia; J.-C. Saut*

The proceedings featured in this book grew out of a conference
attended by 40 applied mathematicians and physicists which was held at
the International Center for Research in Mathematics in Luminy, France,
in May 1995. This volume reviews recent developments in the mathematical
theory of water waves. The following aspects are considered: modeling of
various wave systems, mathematical and numerical analysis of the full
water wave problem (the Euler equations with a free surface) and of
asymptotic models (Korteweg-de Vries, Boussinesq, Benjamin-Ono,
Davey-Stewartson, Kadomtsev-Petviashvili, etc.), and existence and
stability of solitary waves.

Features:

- The latest developments in the theory of water waves.
- Rigorous and formal results.
- Papers from world-renowned experts in the field.

#### Readership

Graduate students and research mathematicians interested in fluid mechanics.

# Table of Contents

## Mathematical Problems in the Theory of Water Waves

- Contents ix10 free
- Preface xi12 free
- An appreciation of T. Brooke Benjamin (1929–1995) xiii14 free
- List of participants xvii18 free
- List of lectures xxi22 free
- Radiation and modulational instability described by the fifth-order Korteweg De Vries equation 126 free
- Numerical simulation of singular solutions of the generalized Korteweg-deVries equation 1742
- Spatially quasi-periodic capillary-gravity waves 3156
- On modulations of weakly nonlinear water waves 4772
- Birkhoff normal forms for water waves 5782
- Remarks on the stability of generalized KP solitary waves 75100
- On the asymptotic integrability of a generalized Burgers equation 85110
- Spatial instabilities and chaos in high-order Hamiltonian standing water waves 99124
- Solitary wave interactions for the fifth-order KdV equation 133158
- Forced Benjamin-Ono equations and related topics 145170
- Nonlinear evolution of water surface waves: The frequency down-shift phenomenon 157182
- Solitary waves on the free surface of a rotating cylindrical flow 173198
- On a generalized Kadomtsev-Petviashvili equation 193218
- A phenomenological description of soliton splitting during run up 211236
- Asymptotic stability of nonlinear bound states in conservative dispersive systems 223248