Symmetry methods for differential equations (applications of Lie groups to differential equations)

This thesis is related with Lie's group analysis for constructing invariant(similarity) solutions of scalar partial differential equations. By employing Lie group analysis, the symmetries of the nonlinear third-order partial differential equation(Korteweg-deVires equation) of motion describing the unidirectional propagation of small amplitude long waves are calculated. The Lie algebra consists of four parameter Lie group of transformations, one being the scaling and the others being translations. Three different types of the solutions are found using these symmetries. Using translations and scalings in x and t coordinates, the hyperbolic type exact solutions are obtained. Finally some boundary value problems are discussed.