Faraday instability in a two-component Bose-Einstein condensate

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates (BECs), we investigate the dynamics of a two-component cigar-shaped BEC subjected to periodic modulation of the strength of the transverse confinement. It is shown that two coupled Mathieu equations govern the dynamics of the system. We found that the two-component BEC in a phase mixed state is relatively more unstable towards pattern formation than the phase segregated state.