Temperature jump in degenerate quantum gases in the presence of a Bose - Einstein condensate

We construct a kinetic equation modeling the behavior of degenerate quantum Bose gases whose collision rate depends on the momentum of elementary excitations. We consider the case where the phonon component is the decisive factor in the elementary excitations. We analytically solve the half-space boundary value problem of the temperature jump at the boundary of the degenerate Bose gas in the presence of a Bose -- Einstein condensate.