The moving law of the scroll wave filament

We investigated the moving law of the scroll wave filament by perturbation arguments, and obtained that, when the normal direction of scroll wave fron t curve surface is similar to that of its filament, the normal speed (noted by alpha) of the filament is relative not only to the curvature (k) of the filament, but also to that k(1) of scroll wave front curve surface, i.e., alpha = epsilon D(k - k(1)) (where D is diffusional coefficient), and irrel ative to the characteristic speed of excitable media. Besides, we also inve stigated the moving law of the filament along the axis direction, and obtai ned the similar result to that of Keener's (J.P. Keener, Physica D31 (1988) 269).