Noether symmetry classification and reductions of the generalized lane-emden equation

Abstract

In this dissertation we perform a Noether point symmetry classification of the generalized Lane-Emden equation which models several phenomena in mathematical physics and astrophysics. We then obtain first integrals of the various cases which admit Noether point symmetries. Moreover, we obtain reduction to quadratures for the cases that admit Noether symmetries. Three new cases are found and these correspond to cases 4.2, 5.1 and 5.2 of chapter 3. We also obtain a two-parameter family of solutions for case 5.1 (when r = 5 and n = 2), whereas in the literature only one-parameter family of solutions is usually given.