Transverse instability of gravity–capillary solitary waves

Abstract

Gravity–capillary solitary waves of depression that bifurcate at the minimum phase speed on water of finite or infinite depth, while stable to perturbations along the propagation direction, are found to be unstable to transverse perturbations on the basis of a long-wave stability analysis. This suggests a possible generation mechanism of the new class of gravity–capillary lumps recently shown to also bifurcate at the minimum phase speed.