Hydrodynamics ofHe3near theATransition

The hydrodynamics of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ in the vicinity of the phase transition is generalized to include an extra variable, the magnitude of the order parameter. Its equation of motion is derived and added to the set of hydrodynamic equations. The effect on the dissipation and dispersion of first, second, and fourth sound is calculated. First sound is found to be anisotropic and a pair of new propagating modes is predicted.