Myroniuk L. Lie symmetries and exact solutions of some nonlinear evolution cross-diffusion systems

The thesis is devoted to constructing Lie symmetries and exact solutions for evolution systems of differential equations, investigation of properties of these solutions. A complete description of Lie symmetries for the Shigesada-Kawasaki-Teramoto system is derived and its new exact solutions are constructed. New exact solutions of the Lotka-Voltera (LV) system with the porous diffusivity and LV type systems with power diffusivities are found. The group classification of a generalized system of thin film equations (TFE) is derived. Lie and non-Lie solutions are constructed for the TFE with the quadratic nonlinearities. Physical and biological interpretation of the solutions obtained are also provided.