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We investigate the dynamics of spin-nonequilibrium electron systems in thehydrodynamic flow regime, when the normal scattering processes, which conservethe total quasi-momentum of the system of electrons and quasi-particles thatinteract with them, dominate over other scattering processes. We obtain a setof spin-hydrodynamic equations for the case of an arbitrary electron spectrumthat varies slowly with the coordinates. Solving the one-dimensional non-linearproblem we found the exact solutions both for the electrical potential in theopen-ends circuit and for the spin-electrical oscillation in an inhomogeneousconducting ring. As we demonstrate, the oscillation characteristics aredifferent in the cases of a magnetic ring and a non-magnetic ring to which thespin polarization was injected. We found also that a voltage between the endsof the open circuit may reveal the presence of an inhomogeneous spinpolarization of the electron density.

Non-Linear Spin Dynamics Of The Electron Liquid In Nanosystems