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chapterNo Access
SOME MATHEMATICAL PROPERTIES OF LONG WAVES
- D. J. BENNEY
Frontiers of Applied Mathematics01 Apr 2007
Preview Abstract
Some aspects of long surface waves are considered. Special attention is focused on the existence of conservation laws for this physical system and related problems.
chapterNo Access
INITIAL VALUE PROBLEM FOR WATER WAVES AND SHALLOW WATER AND LONG WAVE APPROXIMATIONS
- T. IGUCHI
Emerging Topics on Differential Equations and Their Applications01 Feb 2013
Preview Abstract
In this article we explain the well-posedness of the initial value problem for water waves, and the shallow water and long wave approximations for water waves. Especially, we explain that the solution of the full water wave problem can be approximated by the solution of the shallow water equations, the Green–Naghdi equations, the KdV equation, the Kawahara equation, the forced KdV equation, and the Benjamin–Ono equation in some scaling regimes.

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