Mei Symmetry Classification and Conservation Laws of a Coupled Lane–Emden–Klein–Gordon–Fock System with Central Symmetry

In this study, we use the Mei symmetry technique to produce conserved quantities for a system of coupled Lane–Emden–Klein–Gordon–Fock equations with central symmetry. Compared with earlier results by Muatjetjeja (2017) (J. Differential Equations, 263 (2017) 8322–8328), we have discovered new types of conserved quantities using the Mei symmetry method. The system under consideration possesses a two-dimensional maximal Noether algebra and a three-dimensional maximal Lie algebra. We have shown that the maximal Mei algebra is four-dimensional, that is, the system admits more Mei symmetries than the classical Lie and Noether symmetry generators. Furthermore, we have used Mei symmetry reduction to produce several exact solutions for the corresponding system. The novel symmetries and conserved quantities that are derived here can be used to gain a deeper understanding of the physical interpretation of the system taken into account.