NONSPIRAL EXCITATION WAVES BEYOND THE EIKONAL APPROXIMATION

Exact nonplanar traveling solutions for the kinematic model of autowav es in excitable media are constructed using a nonlinear velocity-curva ture relation that is more realistic than the linear (eikonal) approxi mation. The physically unrealistic self-crossing fronts, found earlier in the eikonal approximation, are replaced by noncrossing fronts with cusplike singularities that are reminiscent of ''cellular'' flame str uctures. The new solutions put restrictions on possible autowave refra ction and reflection regimes found in the eikonal approximation. A pos sible role of the unstable branch of the velocity-curvature relation i n removing the cusplike singularities from the present solutions is di scussed.