A new application of the Korteweg–de Vries Benjamin-Ono equation in interfacial electrohydrodynamics

Abstract

We consider waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. We use perturbation theory to identify canonical scalings and to derive a Korteweg–de Vries Benjamin-Ono equation arising in interfacial electrohydrodynamics. When the Bond number is equal to 1∕3, dispersion disappears and the equation reduces to the Benjamin-Ono equation. In the additional limit of vanishing electric fields, we show how to obtain a new evolution equation that contains third- and fifth-order dispersion as well as a nonlocal electric field term.