A computer-assisted study of pulse dynamics in anisotropic media

J. Krishnan, K. Engelborghs, M. Bär, K. Lust, D. Roose, I. G. Kevrekidis

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Abstract

This study focuses on the computer-assisted stability analysis of travelling pulse-like structures in spatially periodic heterogeneous reaction-diffusion media. The physical motivation comes from pulse propagation in thin annular domains on a diffusionally anisotropic catalytic surface. The study was performed by computing the travelling pulse-like structures as limit cycles of the spatially discretized PDE, which in turn is performed in two ways: a Newton method based on a pseudospectral discretization of the PDE, and a Newton-Picard method based on a finite difference discretization. Details about the spectra of these modulated pulse-like structures are discussed, including how they may be compared with the spectra of pulses in homogeneous media. The effects of anisotropy on the dynamics of pulses and pulse pairs are studied. Beyond shifting the location of bifurcations present in homogeneous media, anisotropy can also introduce certain new instabilities.

Original languageEnglish (US)
Pages (from-to)85-110
Number of pages26
JournalPhysica D: Nonlinear Phenomena
Volume154
Issue number1-2
DOIs
StatePublished - Jun 1 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Keywords

  • Continuous spectrum
  • Newton-Picard method
  • Pulse dynamics
  • Reaction-diffusion media

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    Krishnan, J., Engelborghs, K., Bär, M., Lust, K., Roose, D., & Kevrekidis, I. G. (2001). A computer-assisted study of pulse dynamics in anisotropic media. Physica D: Nonlinear Phenomena, 154(1-2), 85-110. https://doi.org/10.1016/S0167-2789(01)00217-2