Gravity solitary waves by minimization: an uncountable family
KeywordsCapillary-gravity water waves, solitary waves, stability, variational methods
AbstractWe 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.
How to Cite
BUFFONI, Boris. Gravity solitary waves by minimization: an uncountable family. Topological Methods in Nonlinear Analysis [online]. 1 December 2009, T. 34, nr 2, s. 339–352. [accessed 1.4.2023].
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