Coupled eigenmodes in a two-component Bose-Einstein condensate

We have studied the elementary excitations in a two-component Bose-Einstein condensate. We concentrate on the breathing modes and find the elementary excitations to possess avoided crossings and regions of coalescing oscillations where both components of the condensates oscillate with same frequency. For large repulsive interactions between the condensates, their oscillational modes tend to decouple due to decreased overlap. A thorough investigation of the eigenmodes near the avoided crossings is presented.