Nonlinear zero sound in a normal Fermi liquid

A nonlinear correction (proportional to the wave amplitude) to the zero-sound velocity is calculated. The growth rate of the amplitude of the second harmonic is also calculated. The result is expressed in terms of the derivative of a Landau function with respect to energy and in terms of its variational derivative with respect to the quasiparticle distribution function. Identities found in this paper make it possible to express the result in terms of the Landau function and its derivative with respect to the pressure, both of which are well known from experiments, in the approximation of the first two spherical harmonics. 5 refs., 1 fig