Nonlinear interaction of first and second sounds in a solid

The nonlinear interaction of first and second sounds in a solid is discussed. Canonical variables are found, and the Hamiltonian is expanded in powers of those variables. The Hamilton equations of motion, including second-order nonlinear terms, are obtained. The vertices and threshold intensities for the scattering of first sound by second sound and for the decay of first sound into two second sounds are calculated. It is shown that the threshold intensity for sound scattering is considerably higher than the decay threshold, which can be an experimentally attainable quantity.