Weiss approach to a pair of coupled non-linear reaction-diffusion equations

Abstract We consider a pair of coupled non-linear partial differential equations describing a biochemical model system. The Weiss algorithm for the Painleve test, that has been succesfully used in mathemathical physics for the KdV equation, Burgers equation, sine-Gordon equation etc., is applied, and we find that the system possesses only the “conditional” Painleve property. We use the outcome of the analysis to construct an auto-Backlund transformation, and we find a variety of one- and two-parameter families of special solutions.