Biomedical subjects

Alidou Mohamadou

Publications and source records attributed to Alidou Mohamadou.

3 recordsLinked to original sources

PubMed2006

Instability criteria and pattern formation in the complex Ginzburg-Landau equation with higher-order terms.

We study the modulational instability and spatial pattern formation in extended media, taking the one-dimensional complex Ginzburg-Landau equation with higher-order terms as a perturbation of the nonlinear Schrödinger equation as a model. By stability analysis for the original partial differential equation, we derive its stability condition as well as the threshold for amplitude perturbations and we show how nonlinear higher-order terms qualitatively change the behavior of the system. The analytical results are found to be in agreement with numerical findings. Modulational instability mediates pattern formation through the lattice. The main feature of the traveling plane waves is its disintegration in pulse train during the propagation through the system.

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PubMed2006

Modulational instability and pattern formation in discrete dissipative systems.

We report in this paper the study of modulated wave trains in the one-dimensional (1D) discrete Ginzburg-Landau model. The full linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vector (q) of the basic states and the wave vector (Q) of the perturbations as free parameters. In particular, it is shown that a threshold exists for the amplitude and above this threshold, the induced modulational instability leads to the formation of ordered and disordered patterns. The theoretical findings have been numerically tested through direct simulations and have been found to be in agreement with the theoretical prediction. We show numerically that modulational instability is also an indicator of the presence of discrete solitons as were early predicted to exist in Ginzburg-Landau lattices.

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PubMed2005

Modulational instability and unstable patterns in the discrete complex cubic Ginzburg-Landau equation with first and second neighbor couplings.

The generation of nonlinear modulated waves is investigated in the framework of hydrodynamics using a model of coupled oscillators. In this model, the separatrices between each pair of vortices may be viewed as individual oscillators and are described by a phenomenological one-dimensional discrete complex Ginzburg-Landau equation involving first- and second-nearest neighbor couplings. A theoretical approach based on the linear stability analysis predicts regions of modulational instability, governed by both the first and second-nearest neighbor couplings. From numerical investigations of different wave patterns that may be driven by the modulational instability, it appears that analytical predictions are correctly verified. For wave number in the unstable regions, an initial condition whose amplitude is slightly modulated breaks into a train of unstable patterns. This phenomenon agrees with the description of amplification of the spectral component of the perturbation and its harmonics, as well.

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