Linearization transformations for nonlinear differential equations

In this master's thesis, firstly the basic definitions and theorems about Lie point symmetry are discussed. In order to obtain Lie symmetries, infinitesimal generators are obtained by applying Lie point symmetry extensions to linear and nonlinear differential equations and using these generators, Lie generators are found. In addition, it is aimed to obtain the symmetries of the equations by linearization and to find the analytical solutions of mathematical physics equations with the help of these symmetries and to make physical interpretations of the equations. As a result, Lie symmetry transformation is used to reach the solutions of mathematical physics equations and nonlinear differential equations and the physical properties of the solutions of the examples are interpreted.