Lagrangian approach to a generalized coupled Lane–Emden system: Symmetries and first integrals

This paper aims to classify a generalized coupled Lane–Emden system and to compute the Noether operators corresponding to a Lagrangian for a generalized coupled Lane–Emden system which occurs in the modelling of several physical phenomena such as pattern formation, population evolution and chemical reactions. In addition the first integrals for the Lane–Emden system are constructed with respect to Noether operators.