Lie Symmetry Method for Solutions of Differential Equations with Applications in Physics

Abstract

Abstract. A mathematical method in pure mathematics (differential geometry) for finding solutions of differential equations is considered. The method is based on constructing a Lie algebra associated to a given system of differential equation, called Lie algebra of the symmetries of the given system. This Lie algebra is a vector space which maps a given solution, such as a constant solution, to another solution, it is a significant tool for finding new solution for system of differential equation specially partial differential equations. Then we will apply it to some differential equations in fluid mechanics and physics.