Diffraction of reaction-diffusion waves: the conformal-mapped eikonal equation

Mark Carter, Faridon Amdjadi, Jagannathan Gomatam

Research output: Contribution to journalArticle

Abstract

The interaction of reaction-diffusion (RD) waves with obstacles is considered. The conformal map transformation of the eikonal equation is used for investigating the behavior of waves in the presence of movable boundaries. It is shown that using the conformal map, the complicated boundary conditions become simple Neumann boundary conditions and can be easily dealt with numerically. The process is applied to diffraction of RD waves by two disks in two dimensions. The approach is extended to three-dimensions and the obstacles considered are 2 two-tori. A stable stationary solution, in the form of an unduloid, trapped between 2 two-tori, is obtained. It is shown that, if the obstacles are located a distance apart, the wave moves away from its stationary position giving rise to regular and irregular motions, depending on the choice of initial solutions.

Original languageEnglish
JournalCommunications in Nonlinear Science and Numerical Simulation
DOIs
Publication statusPublished - 1 Jun 2006

Keywords

  • diffraction; standing waves; travelling and chaotic waves
  • applied mathematics
  • conformal-mapped eikonal equation

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