Lie symmetries and solutions of reaction diffusion systems arising in biomathematics

In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u, v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in several biological problems and in population dynamics. By using weak equivalence transformation the principal Lie algebra, LP, is written and the classifying equations obtained. Then the extensions of LP are derived and classified with respect to Γ(v) and H(u, v). Some wide special classes of special solutions are carried out.