  We investigate dynamics in two-component Bose-Einstein condensates in the
context of coupled Gross-Pitaevskii equations and derive results for the
evolution of the total density fluctuations. Using these results, we show how,
in many cases of interest, the dynamics can be accurately described with an
effective one-component Gross-Pitaevskii equation for one of the components,
with the trap and interaction coefficients determined by the relative
differences in the scattering lengths. We discuss the model in various regimes,
where it predicts breathing excitations, and the formation of vector solitons.
An effective nonlinear evolution is predicted for some cases of current
experimental interest. We then apply the model to construct quasi-stationary
states of two-component condensates.
