Author(s)

P. Barrera, T. Brugarino & L. Pignato

Abstract

Analytic solutions of two coupled reactiondiffusion equations P. Barrera1 , T. Brugarino2 & L. pignato3 ' ~ i p . di Meccanica e Aeronautica 'Dip. di Matematica ed Applicazioni j ~ i p . di Ricerche Energetiche ed Ambientali, Facoltu d'zngegneria, Italy Abstract The aim of this paper is to obtain a set of exact solutions for two coupled reaction-diffusion equations. In order to obtain exact solutions we use the group analysis and the truncated Painlev6 analysis. 1 Introduction The macroscopic formulation of 1;wo ficlds reaction-diffusion model considers thc two fields u(z> t) and v(x, t) whose evolution is governcd by system of equations: whcrc D1(x) and Dz(x) are thc diffusion coefficients, XI and Xp are the reaction cocfficicnts and subscripts dcnotc the partial dcrivativcs. These nonlinear cquations havc been used to dcscribc a wide class of systems, raging from biological morphogencsis to hctcrogcncous chemical rcactions: in particular the phenomena of diffusion of pollutants in the cnv

Keywords