Absrtract. Group classification of systems of two coupled nonlinear reaction-diffusion equation with a general diffusion matrix started in papers [1], [2] is completed in present paper where all non-equivalent equations with triangular diffusion matrix are classified. In addition, symmetries of diffusion systems with nilpotent diffusion matrix and additional first order derivative terms are des...

Firstly, using a series of transformations, the Brusselator reaction diffusion model is reduced into a nonlinear reaction diffusion equation, and then through using Exp-function method, more new exact solutions are found which contain soliton solutions. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The results show the reliability and effic...