Stability limits of spirals and traveling waves in nonequilibrium media

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Abstract
We show that the Eckhaus instability for traveling waves is of convective nature and does not directly lead to absolute instability. As a consequence spiral waves remain stable in a larger range than expected previously, transition to defect-mediated turbulence can be delayed beyond the Benjamin-Feir limit, and the occurrence of phase turbulence can be made plausible. We calculate the onset of absolute instability using the complex Ginzburg-Landau equation and verify the results by simulations.