Symmetry analysis of differential equations

Obtaining solutions to differential equations plays an important role in mathematics, physics, engineering, and many other branches of science because natural events can be examined by making a mathematical model. It is necessary to analyze these physical events to find the solutions of differential equations expressed as mathematical models. There are different methods that provide solutions to differential equations. Thanks to these methods, two different differential equation solutions can be obtained: analytical and numerical. Analytical solutions provide the equation exactly, that is, solutions that do not contain any errors, therefore they are of great importance. One of the most important methods that provide analytical solutions is Lie symmetry analysis. In this thesis, first of all, the basic concepts are discussed, how Lie symmetries can be obtained is examined, and examples of applications for finding these symmetries for physical equations are given