On the symmetry analysis and conservation laws of the (1 + 1)-dimensional Hénon-Lane-Emden system

Abstract

We carry out a complete Lie symmetry analysis and Noether symmetry classification of the (1 + 1)?dimensional H urn:x-wiley:mmma:media:mma4076:mma4076-math-0004non-Lane-Emden system. It is shown that the principal Lie algebra, which is one dimensional, extends in several cases. It is also shown that four main cases transpire in the Noether classification with respect to the Lagrangian. In addition, conservation laws for the H urn:x-wiley:mmma:media:mma4076:mma4076-math-0005 non-Lane-Emden system are constructed. Furthermore, we briefly discuss the importance and the physical interpretation of these conserved vectors.