Nonlinear surface waves in conducting liquids subjected to normal electric fields

The propagation of weakly nonlinear waves on the surface of a shallow viscous conducting liquid layer stressed by a normal electric field is examined. By using a multiple-scale analysis, a Burgers-Korteweg-de Vries equation is obtained. A solution to this equation describing the nonlinear evolution of a kink is explicitly exhibited. For a given value of the imposed electric field, viscous losses can be compensated by injecting electrical energy, and the equation reduces to the Korteweg-de Vries equation, thus showing the possibility of sustaining solitons of permanent amplitude.<>