Coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry: Symmetries and conservation laws

A complete symmetry group classification of a coupled Lane-Emden-Klein-Gordon-Fock system with central symmetry is carried out. This system is a natural two-components generalization of the Klein-Gordon-Fock system with central symmetry. Moreover, conservation laws for the system are obtained. Some interesting physical conclusions related to the derived conserved vectors are discussed.