The shock waves in relativistic superfluid

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We consider the discontinuities in a two-constituent relativistic superfluid. In the acoustic limit they degenerate into the first and second sound which are independent up to the second-order linear approximation. Inclusion of the quadratic deviations relates to the small-amplitude shock. Particularly we consider a plane shock at low temperature when the phonon excitations contribute to the normal constituent. So we found the generalization of the temperature increment and acoustic wave velocity in relativistic superfluid. The fourth sound speed is also calculated.