Simple waves in a two-component Bose-Einstein condensate

We consider dynamics of simple waves in a two-component Bose-Einstein condensates. The evolution of the condensate is described by the Gross-Pitaevskii equations which can be reduced for simple wave solutions to a system of ordinary differential equations which coincide with those derived by Ovsyannikov for the two-layer fuid dynamics. We solve the Ovsyannikov system for two typical situations of large and small difference between inter-species and intra-species nonlinear interaction constants. Our analytic results are confirmed by numerical simulations.