  In ferromagnetic materials, the rich dynamics of magnetic domain walls (DWs)
under magnetic field or current have been successfully described using the
well-known q-{\phi} analytical model. We demonstrate here that this simple
unidimensional model holds for multiple-sublattice materials such as
ferrimagnetic alloys or synthetic antiferromagnets (SAF) by using effective
parameters, and is in excellent agreement with double-lattice micromagnetic
simulations. We obtain analytical laws for the DW velocity and internal
precession angle as a function of net magnetisation for different driving
forces (magnetic field, spin transfer and spin-orbit torques) and different
propagation regimes in ferrimagnetic alloys and SAFs. The model predicts that
several distinctive dynamical features occur near or at the magnetic and the
angular compensation points when the net magnetization or the net angular
momentum of the system vanishes, and we discuss the experimental observations
that have been reported for some of them. Using a higher degree-of-freedom
analytical model that accounts for inter-sublattice distortions, we give
analytical expressions for these distortions that agree with the micromagnetic
simulations. This model shows that the DW velocity and precession rate are
independent of the strength of the inter-sublattice exchange coupling, and
justifies the use of the simpler effective parameters model.
