Nonlinear spin dynamics in superfluidHe3

A previous approach to spin dynamics in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is generalized to the nonlinear regime, where the direction of the order parameter has large deviations from its equilibrium position. The results are used to study the hydrodynamic regime, to derive an equation for the nonlinear regime in the ringing experiments, and to consider the nonlinear effects arising in spin-echo experiments for small tipping angles. The results for the NMR linewidths (in the linear regime) are compared with a very recent work of Leggett and Takagi. Finally, the behavior of these linewidths is investigated at low temperature, where the hydrodynamic assumption $\omega \tau \ll 1$ is no longer valid.