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The problem of interest in this article are waves on a layer of finite depthgoverned by the Euler equations in the presence of gravity, surface tension,and vertical electric fields. Perturbation theory is used to identify canonicalscalings and to derive a Kadomtsev-Petviashvili equation withan additionalnon-local term arising in interfacial electrohydrodynamics.When the Bond numberis equal to 1/3, dispersion disappears and shock waves could potentially form.In the additional limit of vanishing electric fields, a new evolution equationis obtained which contains third and fifth-order dispersion as well as anon-local electric field term.

Linear and Nonlinear Surface Waves in Electrohydrodynamics