| In the literature there are quite a few elegant approaches which have been proposed to find the first integrals of nonlinear differential equations. Recently, the modified Prelle---Singer method for finding the first integrals of second-order nonlinear ordinary differential equations (ODEs) has attracted considerable attention. Many researchers used this method to derive the first integrals to various systems. In this thesis, we are concerned with the first integrals for reaction-diffusion systems with a nonlinear rate of growth. Under certain parametric conditions we express the first integrals explicitly by applying an analytical method as well as the modified Prelle---Singer method. |
