Applications of Lie algebras to Conservation laws of Physics

Abstract

The main purpose of this work is to study the applications of Lie algebras up to Conservation Laws of Physics, Here we use the idea of symmetry Lie algebras to exploit a new method for solving partial differential equations, by calculating symmetry of PDE's system in terms of its Lie's algorithm. In fact when the equation admits solvable Lie algebras, the ideals of the algebra can be used to perform the reduction.