SPATIAL DOPPLER ANOMALY IN AN EXCITABLE MEDIUM

We consider a two-dimensional steady spiral wave in a singly diffusive FitzHugh-Nagumo medium. When perturbed by a uniform external field, t he spiral will, in general, display a drifting motion as well as a spa tial deformation with Doppler-like features. The present work demonstr ates the existence of a radical departure from the conventional moving -source Doppler deformation of the wave pattern in space, even to firs t order in the perturbation. In particular, the maximal shrinking of t he wavelength can occur in a direction very different from the drift i tself; the anomalous direction of the shift amounts to a zeroth-order effect in the perturbation. We present a simple renormalization-based formula for this effect, as well as the results of some numerical simu lations; theory and simulations are in good agreement. The formula inv olves dispersion properties of the one-dimensional unperturbed system. The basic technique is related to Zykov's derivation of the curvature -speed formula for a wave front. There exists a Doppler anomaly in tim e as well, but it is less conspicuous than the spatial one because it is of second order in the perturbation.