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 drop like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.