Figure 1: Selected profiles of quasi-soliton solutions for the FitzHugh-Nagumo kinetics, in co-moving frames of reference.

Left column: two-component model with self- and cross-diffusion. Right column: corresponding reconstructed three-component model with self-diffusion only. The values of the parameter a are given to the left of the panels, for other parameters see the text. The coordinate x − xc is in the comoving frame of reference, see text for detail. For each case, two profiles are shown at the moments t = t1 and t = t2 separated by an interval t2 − t1 = 150; however, the consecutive profiles are only different for a = 0.07 case, as in the other two cases, the waves have steady shapes (see also Apple QuickTime movies corresponding to these regimes in Supplementary information).