Heterogeneous versus discrete mapping problem - art. no. 056624

We propose a method for mapping a spatially discrete problem. stemming from the spatial discretization of a parabolic or hyperbolic partial differenti al equation of gradient type, to a heterogeneous one with certain comparabl e dynamical features pertaining. in particular, to coherent structures. We focus the analysis on a (1 + 1)-dimensional phi (4) model and confirm the t heoretical predictions numerically. We also discuss possible generalization s of the method and the ensuing qualitative analogies between heterogeneous and discrete systems and their dynamics.