DIPLOMA THESIS SYMMETRIES AND CONSERVATION LAWS OBTAINED BY LIE GROUP ANALYSIS FOR CERTAIN PHYSICAL SYSTEMS

The formal model of physical systems is typically made in terms of differential equations. Conservation laws can be found for any system of linear or non-linear differential equations, based on the concept of adjoint equations. Provided that the number of equations is equal to the number of variables, the adjoint equations for a system is used for construction of Lagrangians. Lie group analysis provides us with a way of finding all the symmetries of the original mathematical model. The symmetries are inher-ited by the adjoint equations. By considering the total system of differential equations together with its adjoint equations, we construct the Lagrangian and once the symmetries are found, Noether’s theorem is used for determin-ing conservation laws. Consequently, for any symmetry found by Lie group analysis a conservation law can be found. The mass of mathematical truth is obvious and imposing; its practical applications, the bridges and steamengines and dynamos, obtrud