The Euler equations in the columnar and rotational approximation: A model equation for asymptotic short capillary-gravity waves

Abstract

From a columnar approximation of the Euler equations of an incompressible fluid with surface tension, we derive in the short-wave approximation a new classical 1+1 dimensional model equation for the motion of the surface. The side-band instability of the Stokes’ waves is analyzed in terms of the physical parameters of the system.