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The ripplon modes of two segregated Bose-Einstein condensates (BECs) confined by one and two hard walls are respectively studied by means of the hydrodynamic approach within the Gross-Pitaevskii (GP) theory. For the system at rest we find that due to the spatial restriction  the dispersion relations are of the form \(\omega  \sim {k^2}\) in low momentum limit for both cases, while for the system in motion parallel to the interface the dispersion relations for both cases are \(\omega  \sim k\) at low momentum limit  and, furthermore,  the system becomes unstable.

Ripplon Modes of Two Segregated Bose-Einstein Condensates in Confined Geometry