ANALYSIS OF DOMAIN-SOLUTIONS IN REACTION-DIFFUSION SYSTEMS

We investigate a standard model for bistable reaction-diffusion-systems, which shares characteristic properties with the van-der-Pol oscillator for distributed generators and the FitzHugh-Nagumo system. In this system we study the effect of a long ranging inhibitor. As a main result we show the existence of two inhomogeneous stationary solutions - the smaller one is always a saddle which corresponds to a critical nucleus, while the larger one arises as a stable solution. In carrying out the linear stability analysis for these solutions, we have to treat the Schrodinger-equation for a double-well potential. This is done approximately by a supersymmetric approach which yields the eigenvalues and eigenfunctions of the Schrodinger-equation. Furthermore we compare our analytical findings with numerical results - especially the occurrence of oscillating solutions is shown.