Reciprocal Transformations of Two-Component Hyperbolic Systems and Their Invariants

Criteria for the equivalence under reciprocal transformations of two-component hyperbolic systems are established in terms of reciprocal invariants. These results are applied to a 1q1-dimensional isentropic gasdynamics system to determine reciprocal equivalence to the canonical system with a polytropic gas law. The four-parameter model pressure-density relations for which this reciprocal equivalence holds are parameterized in terms of the Lagrangian signal speed.