Exact circular static patterns in nonlinear-wave?sustaining media

MAURICIO BELLINI; ROBERTO DEZA

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-BASIC TOPICS IN PHYSICS

SOC ITALIANA FISICA

Lugar: Bologna; Año: 1998 vol. 113 p. 1231 - 1238

1594-9982

We have recently introduced a recipe to obtain exact solutions of reactiondiffusion (RD) equations with variable diffusion coefficient D(). This is achieved by mapping them onto stationary Schr¨odinger ones?with the form of the potential at our disposal?and exploiting the knowledge of the ground-state solutions of a quasiexactly solvable Schr¨odinger potential. Only a qualitative information on the spatio-temporal dependence of D is required. In the present work we show that the method also applies to nonlinear reacting systems such that the nonlocal term contains an integer power n of the spatial derivative (the usual RD systems correspond to n = 1). An example is worked through, proposing as Schr¨odinger potential a Morse-like one.