Weiss-approach to 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 Painleé test, that has been succesfully used in mathematical physics for the KdV-equation, Burgers equation, the sine-Gordon equation etc., is applied, and we find that the system possesses only the "conditional" Painlevé property. We use the outcome of the analysis to construct an auto-Bäcklund transformation, and we find a variety of one and two-parameter families of special solutions.