A singular integrable equation from short capillary-gravity waves

by Neveu, Andre

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 integrable classical 1+1 dimensional field theory for the motion of the surface. Together with a Lorentz invariance, this system has the novel feature of solutions which become multiple valued in finite time.