Nonlinear Modes of Liquid Drops as Solitary Waves

The nonlinear dynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg--de Vries (KdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such ``rotons'' were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to droplike systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.