Global bifurcation of capillary-gravity dark solitary waves on the surface of a conducting fluid under normal electric fields

This article is concerned with capillary-gravity waves travelling on the interface of a dielectric gas and a conducting fluid under the effect of a vertical electric field. A boundary integral equation method is employed to compute fully nonlinear steady travelling wave solutions. The global bifurcation diagram of periodic waves, solitary waves, generalised solitary waves and dark solitary waves is presented and discussed in detail.