Waves on an interface between two phase-separated Bose-Einstein condensates

We examine waves localized near a boundary between two weakly segregated Bose-Einstein condensates, In the case of a wavelength of the order of or larger than the thickness of the overlap region the variational method is used. The dispersion laws for the two oscillation branches are found in analytic form. The opposite case of a wavelength much shorter than the healing length in the bulk condensate is also discussed.