Abstract
The dynamics of wave fronts in two dimensional excitable media is analytically studied. By means of the asymptotic perturbation method for wave fronts in reaction-diffusion systems, we derive a space-derivative Burgers' equation which governs the shape of boundary layers and their propagation. Application of Lie group analysis of differential equations yields group-invariant solutions of this equation and their classification. Some classes of the group-invariant solutions determine the remarkable patterns; expanding circle waves, rotating spiral waves. Initial value problems for the Burgers' equation are also studied, and a spiral wave is shown to be asymptotically realized under some proper boundary conditions.
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