José Fernando Bustamante-Castañeda , Gustavo Cruz-Pacheco
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引用次数: 0
Abstract
In this work, we study the phenomenon of propagation failure for fronts in a bistable reaction–diffusion equation on a lattice in one and two dimensions. Using asymptotic methods and modulation theory, we approximate the anchoring region in the parameter space defined by the coupling coefficient and the bistability parameter. For the one-dimensional case, modulation theory yields a periodic, time-dependent velocity of the wavefront, governed by a Peierls–Nabarro potential. We provide a simple explanation for a numerical observation made in previous work by Mallet-Paret, Hoffman and Mallet-Paret (2010), regarding the fact that a stationary vertical wavefront begins to advance when its direction is perturbed. We also present numerical evidence demonstrating the accuracy of our approximations.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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