Nonlinear spin dynamics of quantum paramagnetic fluids.

The spin dynamics of Fermi liquids and dilute polarized gases can be reduced in the nonlinear limit to a dissipative Heisenberg ferromagnet model. We obtain all the quasi-periodic elementary excitations for such a model exactly using an inverse Abel- Jacobi transformation. Previously known spin wave and soliton modes appear here as limiting cases of more general excitation which can be classified in terms of the number N of dynamical variables. In increasing degree of complexity they are spin waves (N = 1), cnoidal waves (N = 2), pulsons (N = 3) and more complex breather modes (N >= 4). In the presence of magnetic field gradients, the spin oscillations, which are spatially localized in the linear limit, can penetrate the magnetic potential barrier for larger nonlinearities with characteristic spatial periodicities.