Auto-Darboux Transformation and Exact Solutions of the Brusselator Reaction Diffusion Model

Firstly, using the improved homogeneous balance method, an auto_Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine_cosine method, more exact solutions are found which contain soliton solutions.