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Mathematical Problems in the Theory of Water Waves
Edited by: F. Dias, Institute Nonlinéare de Nice, Valbonne, France, J.-M. Ghidaglia, Ecole Normale Supérieure, Cachan, France, and J.-C. Saut, Universitéde Paris-Sud, Orsay, France
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Contemporary Mathematics
1996; 235 pp; softcover
Volume: 200
ISBN-10: 0-8218-0510-X
ISBN-13: 978-0-8218-0510-7
List Price: US$67
Member Price: US$53.60
Order Code: CONM/200
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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

  • I. Bakholin and A. Il'ichev -- Radiation and modulational instability described by the fifth-order Korteweg-De Vries equation
  • J. e. al. et al. -- Numerical simulation of singular solutions of the generalized Korteweg-de Vries equation
  • T. J. Bridges and F. Dias -- Spatially quasi-periodic capillary-gravity waves
  • T. Colin, F. Dias, and J.-M. Ghidaglia -- On modulations of weakly nonlinear water waves
  • W. Craig -- Birkhoff normal forms for water waves
  • A. d. Bouard and J.-C. Saut -- Remarks on the stability of generalized KP solitary waves
  • A. S. Fokas and L. Luo -- On the asymptotic integrability of a generalized Burgers equation
  • M. Glozman and Y. Agnon -- Spatial instabilities and chaos in high-order Hamiltonian standing water waves
  • B. Malomed and J.-M. Vanden-Broeck -- Solitary wave interactions for the fifth order KdV equation
  • Y. Matsuno -- Forced Benjamin-Ono equations and related topics
  • C. Shankrani, C. Kharif, and J. Poitevin -- Nonlinear evolution of water surface waves: The frequency down-shift phenomenon
  • S. M. Sun -- Solitary waves on the free surface of a rotating cylindrical flow
  • M. M. Tom -- On a generalized Kadomtsev-Petviashvili equation
  • E. v. Groesen -- A phenomenological description of soliton splitting during run up
  • M. I. Weinstein -- Asymptotic stability of nonlinear bound states in conservative dispersive systems
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