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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.

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