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

@inproceedings{Brusch2001CD,
  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},
  year={2001}
}
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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View 5 Excerpts
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View 2 Excerpts

References

Publications referenced by this paper.
Showing 1-10 of 19 references

M

L. Brusch, M. G. Zimmermann
van Hecke, M. Bär and A. Torcini, Phys. Rev. Lett. 85, 86 • 2000

Nature 379

Q. Ouyang, J. M. Flesselles
143 (1996); Q. Ouyang, H. L. Swinney and G. Li, Phys. Rev. Lett. 84, 1047 (2000); L. Q. Zhou and Q. Ouyang, Phys. Rev. Lett. 85, 1650 • 2000
View 2 Excerpts

Physica D 135

M. Or-Guil, I. G. Kevrekidis, M. Bär
154 • 2000
View 1 Excerpt

, unpublished results . [ 8 ] N . Garnier and A . Chiffaudel

A. Chiffaudel N. Garnier, F. Daviaud
Phys . Rev . Lett . • 1998

Chemical Oscillations

Y. Kuramoto
Waves and Turbulence (Springer, 1984, Berlin); P. Manneville, Dissipative structures and Weak Turbulence (Academic Press, 1990, San Diego); T. Bohr, M. H. Jensen, G. Paladin and A. Vulpiani, Dynamical systems approach to turbulence (Cambridge Univ. Press) • 1998
View 1 Excerpt

B

E. Doedel, A. Champneys, T. Fairgrieve, Y. Kusnetsov
Sandstede and X. Wang, AUTO97:Continuation and bifurcation software for ordinary differential equations • 1997
View 1 Excerpt

Hernández - Garćıa , A . Amengual and M . San Miguel

E. R. Montagne
Phys . Rev . E • 1996

Quasiperiodische Lösungen der eindimensionalen komplexen Ginzburg-Landau Gleichung

G. Hager
Diploma Thesis, University of Bayreuth, Germany • 1996
View 1 Excerpt

Nonlinearity 7

H. Chaté
185 (1994); p. 33 in P. E. Cladis and Palffy- Muhoray (Eds.),“Spatio-Temporal Pattern Formation in Nonequilibrium Complex Systems” • 1995

Phys

F. Daviaud, J. M. Vince
Rev. E 48, 4432 • 1993

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