THE EIKONAL APPROXIMATION TO EXCITABLE REACTION-DIFFUSION SYSTEMS - TRAVELING NONPLANAR WAVE-FRONTS ON THE PLANE

Exact, non-planar travelling solutions of the eikonal equation on an i nfinite plane are presented for the first time. These solutions are ma tched to produce corrugated wave fronts and patterns such as 'spot' so lutions as well as extended parabolic type wave fronts. The stability of these solutions is also analysed. The variational equation which be longs to a generalised Wangerin class of differential equations is sol ved, first with the aid of the Liouville-Green approximation for the e stimated eigenvalues characterising stability and then by a more elabo rate shooting-matching method. All of the three types of travelling so lutions are found to be geometrically stable. It is suggested that som e of these predictions are experimentally testable.