Sound-like oscillations in the polar phase of superfluid $^3$He in a nematic aerogel

The acoustic spectrum of the polar phase of superfluid $^3$He in nematic aerogel has been studied. An equation determining the dispersion of sound oscillations of the system has been derived. Solutions of the system have been obtained for low-frequency oscillations, whose propagation velocity is much lower than the speed of first sound in pure $^3$He, for directions along and across the anisotropy axis of the aerogel. In the same approximation, a solution for purely shear oscillations of the system has been found under special boundary conditions corresponding to an incompressible liquid surrounding the system. The temperature dependence of the found frequencies has been compared with the existing experimental data.