EXACT CIRCULAR STATIC PATTERNS IN NONLINEAR-WAVE-SUSTAINING MEDIA

We have recently introduced a recipe to obtain exact solutions of reac tion-diffusion (RD) equations with variable diffusion coefficient D(ph i). This is achieved by mapping them onto stationary Schrodinger ones- with the form of the potential at our disposal-and exploiting the know ledge of the ground-state solutions of a quasiexactly solvable Schrodi nger potential. Only a qualitative information on the spatio-temporal dependence of D is required. In the present work we show that the meth od also applies to nonlinear reacting systems such that the nonlocal t erm contains an integer power n of the spatial derivative (the usual R D systems correspond to n = 1). An example is worked through, proposin g as Schrodinger potential a Morse-like one.