Relativistic perfect fluids: integrability of the classical Taub system

It is established that the classical Taub system governing isentropic planar motions of perfect fluids in special relativity may be formulated entirely in soliton-theoretic terms. The well-established tools of integrable systems theory may therefore be used to produce large classes of solutions given in parametric form. As an illustration, the general solution of the Taub system associated with a privileged pressure-density constitutive law is generated by applying a binary Darboux transformation to the seed solution of the Taub system descriptive of extreme fluids.