Similarity reductions and integrability for the Brusselator reaction-diffusion model with symbolic computation

The direct reduction method and computerized symbolic computation are extended to the Brusselator reaction-diffusion model, which describes a biochemical system and consists of two coupled nonlinear partial differential equations. New similarity reductions are obtained, which could be of biochemical interest. The resulting nonlinear ordinary differential equation in one dynamical variable cannot be transformed into any of the six standard forms which have solutions in terms of the Painlevé transcendents. Thus, the Brusselator model is not integrable according to the Painlevé conjecture.