If intra-species nonlinear interaction constants in a two-component Bose-Einstein condensate have close values, then dynamics of the condensate reduces to the so-called polarization modes with preservation of the total density of two components. In dispersionless limit this dynamics coincides with Ovsyannikov?s ?model III? for dynamics of a two-layer fluid. We derive nonlinear wave equations for these polarization waves in BEC with account of dispersion and show that the resulting equations coincide with the Landau-Lifshitz equations for magnetics with easy-plane anisotropy. Periodic solutions and corresponding Whitham modulation equations are obtained. They are applied to the problem of evolution of initial discontinuities in distributions of densities and relative velocities of the condensate components. Relations of the theory to the current experiments are discussed.