Group classification of the generalized Emden-Fowler-type equation

摘要

We perform the Lie group classification of the Emden-Fowler-type equation xu '' + nu' + x(v)F(u) = 0, which arises in several applications. These include the theory of stellar structure, the thermal behaviour of a spherical cloud of gas, isothermal gas spheres and the theory of thermionic currents. Seven cases arise for the possible extension of the principal Lie algebra, which in this case is trivial. Three new cases occur for which we have non-trivial Lie point symmetry algebra. We compare these cases with the Noether symmetry cases. Moreover, we also make comparisons with the partial Noether operators. Finally for three cases we reduce the Emden-Fowler-type equation to quadratures.