  We investigate the propagation of spin waves in two-component mixtures of
one-dimensional Bose gases interacting through repulsive contact potentials. By
using quantum Monte Carlo methods we calculate static ground-state properties,
such as the spin susceptibility and the spin structure factor, as a function of
both the intra-species and inter-species coupling strength and we determine the
critical parameters for phase separation. In homogeneous mixtures, results of
the velocity of spin waves and of its softening close to the critical point of
phase separation are obtained by means of a sum-rule approach. We quantify the
non-dissipative drag effect, resulting from the Andreev-Bashkin current-current
interaction between the two components of the gas, and we show that in the
regime of strong coupling it causes a significant suppression of the spin-wave
velocity.
