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.
Josephine Anna Eleanor Hughes, Nana Obayashi
Tobias Kippenberg, Rui Ning Wang, Mikhail Churaev, Xinru Ji, Aleksandr Tusnin, Kenichi Komagata, Junqiu Liu, Alexey Tikan