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Heterogeneous versus discrete mapping problem

2001; American Physical Society; Volume: 64; Issue: 5 Linguagem: Inglês

10.1103/physreve.64.056624

1538-4519

P. G. Kevrekidis, Ioannis G. Kevrekidis,

Differential Equations and Numerical Methods

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