Mathematical Problems in the Theory of Water Waves: A Workshop on the Problems in the Theory of Nonlinear Hydrodynamic Waves, May 15-19, 1995, Luminy, France

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American Mathematical Soc., 1996 - Science - 235 pages
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, and papers from world-renowned experts in the field.
 

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Contents

Radiation and modulational instability described by the fifthorder Korteweg De Vries equation
1
Numerical simulation of singular solutions of the generalized KortewegdeVries equation
17
Spatially quasiperiodic capillarygravity waves
31
On modulations of weakly nonlinear water waves
47
Birkhoff normal forms for water waves
57
Remarks on the stability of generalized KP solitary waves
75
On the asymptotic integrability of a generalized Burgers equation
85
Spatial instabilities and chaos in highorder Hamiltonian standing water waves
99
Solitary wave interactions for the fifthorder KdV equation
133
Forced BenjaminOno equations and related topics
145
The frequency downshift phenomenon
157
Solitary waves on the free surface of a rotating cylindrical flow
173
On a generalized KadomtsevPetviashvili equation
193
A phenomenological description of soliton splitting during run up
211
Asymptotic stability of nonlinear bound states in conservative dispersive systems
223
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