  The linear response of a neutron spin-triplet superfluid onto external weak
axial-vector field is studied for the case of $^{3}P_{2}$ pairing with a
projection of the total angular momentum $m_{j}=0$. The problem is considered
in the BCS approximation discarding Fermi-liquid effects. The anomalous
axial-vector vertices of neutron quasiparticles possess singularities at some
frequencies which specify existence of undamped spin-density waves in the
Cooper condensate. The spin waves are of a low excitation energy and are
kinematically able to decay into neutrino pairs through neutral weak currents.
We evaluate the neutrino emissivity from the spin wave decays in the bulk
neutron superfluid in old neutron stars. This calculation predicts significant
energy losses from within a neutron star at lowest temperatures when all other
mechanisms of neutrino emission are killed by the neutron and proton
superfluidity.
