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Article Dans Une Revue Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Année : 2009

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

Résumé

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.

Dates et versions

hal-00489381 , version 1 (04-06-2010)

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L. Nana, A.B. Ezersky, I. Mutabazi. Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, 2009, 465 (2107), pp.2251-2265. ⟨10.1098/rspa.2009.0002⟩. ⟨hal-00489381⟩
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