Gravity solitary waves by minimization: an uncountable family

Boris Buffoni


We improve and simplify the minimization method for solitary
waves in two cases: firstly, when the surface tension is weak (that is,
the Bond number is $< 1/3$) and the depth is finite, and secondly,
when the depth is infinite.
In a previous work on the first case,
minimizers were shown to exist for a sequence tending to $0$
of values of the horizontal impulse. The main difficulty
is that strict subadditivity in the concentration-compactness
method is unsettled.
Here we observe in both examples
that strict subadditivity nevertheless holds for
a set of horizontal impulses of positive measure and the related
propagation speeds are estimated from above.


Capillary-gravity water waves; solitary waves; stability; variational methods

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