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Abstract
The increased interest in water wave theory over the last decade has been motivated,
arguably, by two themes: rst, noticeable progress in the investigation of the
governing equations for water waves (well-posedness issues, as well as in-depth qualitative
studies of regular wave patterns{see the discussion and the list of references
in [1, 17], respectively in [9]), and secondly, by the derivation and study of various
model equations that, although simpler, capture with accuracy the prominent features
of the governing equations in a certain physical regime. The two themes are
intertwined with one another.
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