EXACT TRAVELING ANNULAR WAVES IN GENERALIZED REACTION-DIFFUSION EQUATIONS

We have recently introduced a semi-inverse method which renders exact static solutions of one-component, one-dimensional reaction-diffusion (RD) equations with variable diffusion coefficient D(phi), requiring a t most qualitative information on the spatial dependence D(x) of the l atter. Through a simple ansatz the RD equations can be mapped onto (st ationary) Schrodinger equations, having the form of the potential stil l at our disposal. In this work we show that the method also applies t o two- and three-dimensional static cases with angular symmetry, as we ll as to (steady) non-static cases. As an illustration we exploit the knowledge of the ground state solutions of a spatially periodic, quasi -exactly solvable Schrodinger potential which is a close relative to t he Poschl-Teller potential, to exhibit a highly non-trivial solution w hich describes outgoing radial waves. (C) 1997 Elsevier Science B.V.