  Rigorous coupled spin-charge drift-diffusion equations are derived from
quantum-kinetic equations for the spin-density matrix that incorporate effects
due to k-linear spin-orbit interaction, an in-plane electric field, and the
elastic scattering on nonmagnetic impurities. The explicit analytical solution
for the induced magnetization exhibits a pole structure, from which the
dispersion relations of spin excitations are identified. Applications of the
general approach refer to the excitation of long-lived field-induced spin waves
by optically generated spin and charge patterns. This approach transfers
methods known in the physics of space-charge waves to the treatment of spin
eigenmodes. In addition, the amplification of an oscillating electric field by
spin injection is demonstrated.
