  We derive solitary-wave solutions within the mean-field approximation in
quasi-one-dimensional binary mixtures of Bose-Einstein condensates under
periodic boundary conditions, for the case of an effective repulsive
interatomic interaction. The particular gray-bright solutions that give the
global energy minima are determined. Their characteristics and the associated
dispersion relation are derived. In the case of weak coupling, we diagonalize
the Hamiltonian analytically to obtain the full excitation spectrum of
"quantum" solitary-wave solutions.
