An approximation to a sharp type solution of a density-dependent reaction-diffusion equation

In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation ut= [(u+εu2)ux]x+u(1-u) in the case of travelling wave solutions (t.w.s. ): u(x,t) = ∅(x-ct). We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively. © 1994.