C D ] 2 2 O ct 2 00 1 Nonlinear Analysis of the Eckhaus Instability : Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient

  title={C D ] 2 2 O ct 2 00 1 Nonlinear Analysis of the Eckhaus Instability : Modulated Amplitude Waves and Phase Chaos with Non-zero Average Phase Gradient},
  author={Lutz Brusch and Alessandro Torcini and Markus B{\"a}r},
We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasiperiodic solutions of the CGLE that emerge near the Eckhaus instability of plane waves and cease to exist due to saddle-node bifurcations (SN). These MAWs can be characterized by their average phase gradient ν and by the spatial period P of the periodic amplitude… CONTINUE READING


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