Phonon gas and changes of shape of second sound wave

A generalized non linear Maxwell-Cattaneo equation is used to study shock waves propagating in a rigid heat conductor at low temperature. Taking into account the experimental values for the second sound velocity, the existence of a critical temperature characteristic of the materials and separating two families of shocks, the “hot” and the “cold” ones, is proved both numerically and analytically. Finally a possible explanation of the distortion of the initial second sound thermal pulse during its propagation is proposed.