The homogeneous Boltzmann equation for a moderator is specialized for isotropic scattering kernels and probed for wave solutions. There emerges a discrete set of wave numbers corresponding to the frequency ω as well as a continuum. The former constitutes a dispersion law having the same form as that based upon PN multigroup theory, but in general, the parameters are now given explicitly by inverse moments of v∑T averaged over distributions determined by the scattering kernel. The accuracy of these constants does not depend upon assumptions regarding the neutron energy spectrum. The waves near the limit of detectability have wave lengths and attenuation lengths of the order of the maximum mean free path. Such attenuation lengths approach the continuum boundary. The waves near the continuum boundary have phase velocities approaching that particle velocity which minimizes ∑T(v). At frequencies above the minimum collision frequency, no discrete waves definitely propagate, but when the frequency is low enough for a set of discrete waves to be generated, their attenuation is always smaller than that of the accompanying continuum so that an asymptotic region exists in which conventional neutron wave measurements can still be carried out. The criterion for the existence of discrete waves at low frequencies is the same as that for the existence of discrete relaxation lengths in an exponential experiment.