  We introduce and solve a semi-classical random walk (RW) model that describes
the dynamics of spin polarization waves in zinc-blende semiconductor quantum
wells. We derive the dispersion relations for these waves, including the
Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the
effects of an electric field applied parallel to the spin polarization
wavevector. In agreement with fully quantum mechanical calculations [Kleinert
and Bryksin, Phys. Rev. B \textbf{76}, 205326 (2007)], the RW approach predicts
that spin waves acquire a phase velocity in the presence of the field that
crosses zero at a nonzero wavevector, $q_0$. In addition, we show that the
spin-wave decay rate is independent of field at $q_0$ but increases as
$(q-q_0)^2$ for $q\neq q_0$. These predictions can be tested experimentally by
suitable transient spin grating experiments.
