TY - JOUR
T1 - Diffraction of reaction-diffusion waves: the conformal-mapped eikonal equation
AU - Carter, Mark
AU - Amdjadi, Faridon
AU - Gomatam, Jagannathan
N1 - <p>Originally published in: Communications in Nonlinear Science and Numerical Simulation (2006), 11 (1), 424-439.</p>
PY - 2006/6/1
Y1 - 2006/6/1
N2 - 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.
AB - 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.
KW - diffraction; standing waves; travelling and chaotic waves
KW - applied mathematics
KW - conformal-mapped eikonal equation
U2 - 10.1016/j.cnsns.2004.08.003
DO - 10.1016/j.cnsns.2004.08.003
M3 - Article
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -