LeHavreV1, Main, Exploration, bibRecord, 000A91

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

Identifieur interne : 000A91 ( Main/Exploration ); précédent : 000A90; suivant : 000A92

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

Auteurs : L. Nana [France] ; A. B. Ezersky [France] ; I. Mutabazi [France]

Source :

RBID : Hal:hal-00489381

Abstract

Experiments in extended systems, such as the counter-rotating Couette–Taylor flow or the Taylor–Dean flow system, have shown that patterns with vanishing amplitude may exhibit periodic spatio-temporal defects for some range of control parameters. These observations could not be interpreted by the complex Ginzburg–Landau equation (CGLE) with periodic boundary conditions. We have investigated the one-dimensional CGLE with homogeneous boundary conditions. We found that, in the ‘Benjamin–Feir stable' region, the basic wave train bifurcates to state with periodic spatio-temporal defects. The numerical results match the observations quite well. We have built a new state diagram in the parameter plane spanned by the criticality (or equivalently the linear group velocity) and the nonlinear frequency detuning.

Url:

https://hal.archives-ouvertes.fr/hal-00489381

DOI: 10.1098/rspa.2009.0002

Affiliations:

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Le document en format XML

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<front><div type="abstract" xml:lang="en">Experiments in extended systems, such as the counter-rotating Couette–Taylor flow or the Taylor–Dean flow system, have shown that patterns with vanishing amplitude may exhibit periodic spatio-temporal defects for some range of control parameters. These observations could not be interpreted by the complex Ginzburg–Landau equation (CGLE) with periodic boundary conditions. We have investigated the one-dimensional CGLE with homogeneous boundary conditions. We found that, in the ‘Benjamin–Feir stable' region, the basic wave train bifurcates to state with periodic spatio-temporal defects. The numerical results match the observations quite well. We have built a new state diagram in the parameter plane spanned by the criticality (or equivalently the linear group velocity) and the nonlinear frequency detuning.</div>
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Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

Source :

Abstract

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