Equations of two-fluid hydrodynamics in the Hubbard model

A set of equations is obtained using stationary and nonstationary superconductivity theories in terms of the Hubbard model. The equations near T _c and for a weak magnetic field have the general form of superconductivity equations with a strongly anisotropic Fermi surface. Calculations are performed using a kinetic equation for quasiparticles. The low-temperature collective excitations in a superconductor are studied. An explicit relationship for the temperature dependence of second sound is obtained.