Group analysis of a hyperbolic Lane–Emden system

In this paper we carry out a complete Noether and Lie group classification of the radial form of a coupled system of hyperbolic equations. From the Noether symmetries we establish the corresponding conserved vectors. We also determine constraints that the nonlinearities should satisfy in order for the scaling symmetries to be Noetherian. This led us to a critical hyperbola for the systems under consideration. An explicit solution is also obtained for a particular choice of the parameters.