  The fully nonlinear dynamics of spin and charge in spin-Calogero model is
studied. The latter is an integrable one-dimensional model of quantum spin-1/2
particles interacting through inverse-square interaction and exchange.
Classical hydrodynamic equations of motion are written for this model in the
regime where gradient corrections to the exact hydrodynamic formulation of the
theory may be neglected. In this approximation variables separate in terms of
dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of
decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi
momenta. We study the dynamics of some non-equilibrium spin-charge
configurations for times smaller than the time-scale of the gradient
catastrophe. We find an interesting interplay between spin and charge degrees
of freedom. In the limit of large coupling constant the hydrodynamics reduces
to the spin hydrodynamics of the Haldane-Shastry model.
