The Euler relativistic gasdynamic system. Chaplygin–Kármán–Tsien laws and substitution principle

A seed class of exact solutions of the Euler system of two-dimensional relativistic gasdynamics is derived with an underlying Chaplygin–Kármán–Tsien type constitutive law. The invariance of the nonlinear relativistic system under multi-parameter reciprocal Bäcklund transformations is applied to generate a wide class of novel associated solutions with a barotropic relation. The latter reduces to the standard Chaplygin–Kármán–Tsien gas law in the non-relativistic limit. An additional invariance of the general relativistic gasdynamics system is established under a substitution principle. The latter represents an extension of a classical result in non-relativistic gasdynamics.