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We examine waves localized near a boundary between two weakly segregatedBose-Einstein condensates. In the case of a wavelength of order of or largerthan the thickness of the overlap region the variational method is used. Thedispersion laws for the two oscillation branches are found in analytic form.The opposite case of a wavelength much shorter than the healing length in thebulk condensate is also discussed.Comment: revtex, 4 pages, 1 figure Results substantially revise

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