Periodic waves in a two-component Bose-Einstein condensate

Periodic waves in a two-component Bose-Einstein condensate are considered with allowance for mixing of components admitted by the interaction between atoms. The possibility of relative motion of the components leads to significant variability of the system dynamics as compared to the case of a single-component condensate. In particular, it was experimentally established that, if one component flows relative to another, waves with counterphase oscillations of the components can be excited in the two-component condensate. A theory of one-phase periodic waves is developed for the case of weak mixing of the components, in which the condensate dynamics is described with sufficiently good precision by a system of Gross-Pitaevskii equations with equal constants of nonlinear interaction between atoms both of the same and different kinds. Both condensates with repulsive and attractive interactions between atoms are considered. The limiting case of waves with constant amplitude is studied in detail. The structure of soliton analogs in these systems is considered. The possibility of applying the proposed theory to description of experimentally observed wavy periodic structures in two-component Bose-Einstein condensate is discussed.