Non-linear propagation of waves on two-dimensional liquid sheets

Abstract

The long time behavior of antisymmetric as well as symmetric waves on a two-dimensional liquid sheet is studied, the effects of the surrounding fluid being taken into account. The non-linear Schrödinger equation governing the wave motion is derived by the method of multiple scales. Modulatory stability, wave-wave interaction and non-linear stability are studied and a possible mechanism accounting for the disintegration of the sheet is found.