Modulation instability and pattern formation in damped molecular systems

Conrad B. Tabi; Alidou Mohamadou; Timoléon C. Kofané

doi:10.1166/jctn.2009.1076

Modulation instability and pattern formation in damped molecular systems

Conrad B. Tabi, Alidou Mohamadou, Timoléon C. Kofané

Physics & Astronomy

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

It is shown that, in the weak amplitude and slow time limits, the dynamics of a damped onedimensional lattice is governed by the modified complex Ablowitz-Ladik (MCAL) equation. We conduct a theoretical analysis of the linear stability based on the MCAL equation, obtaining the modulational instability (Ml) criterion. We show that, if the wave amplitude exceeds a certain threshold value, the initial solution breaks into pulse train. Energy localization via Ml is also investigated through computer simulations. We find very good quantitative agreement between the theoretical analysis and the numerical simulations of the MCAL equation for the Ml.

Original language	English
Pages (from-to)	583-592
Number of pages	10
Journal	Journal of Computational and Theoretical Nanoscience
Volume	6
Issue number	3
DOIs	https://doi.org/10.1166/jctn.2009.1076
Publication status	Published - Mar 1 2009

All Science Journal Classification (ASJC) codes

Chemistry(all)
Materials Science(all)
Condensed Matter Physics
Computational Mathematics
Electrical and Electronic Engineering

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title = "Modulation instability and pattern formation in damped molecular systems",

abstract = "It is shown that, in the weak amplitude and slow time limits, the dynamics of a damped onedimensional lattice is governed by the modified complex Ablowitz-Ladik (MCAL) equation. We conduct a theoretical analysis of the linear stability based on the MCAL equation, obtaining the modulational instability (Ml) criterion. We show that, if the wave amplitude exceeds a certain threshold value, the initial solution breaks into pulse train. Energy localization via Ml is also investigated through computer simulations. We find very good quantitative agreement between the theoretical analysis and the numerical simulations of the MCAL equation for the Ml.",

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T1 - Modulation instability and pattern formation in damped molecular systems

AU - Tabi, Conrad B.

AU - Mohamadou, Alidou

AU - Kofané, Timoléon C.

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Y1 - 2009/3/1

N2 - It is shown that, in the weak amplitude and slow time limits, the dynamics of a damped onedimensional lattice is governed by the modified complex Ablowitz-Ladik (MCAL) equation. We conduct a theoretical analysis of the linear stability based on the MCAL equation, obtaining the modulational instability (Ml) criterion. We show that, if the wave amplitude exceeds a certain threshold value, the initial solution breaks into pulse train. Energy localization via Ml is also investigated through computer simulations. We find very good quantitative agreement between the theoretical analysis and the numerical simulations of the MCAL equation for the Ml.

AB - It is shown that, in the weak amplitude and slow time limits, the dynamics of a damped onedimensional lattice is governed by the modified complex Ablowitz-Ladik (MCAL) equation. We conduct a theoretical analysis of the linear stability based on the MCAL equation, obtaining the modulational instability (Ml) criterion. We show that, if the wave amplitude exceeds a certain threshold value, the initial solution breaks into pulse train. Energy localization via Ml is also investigated through computer simulations. We find very good quantitative agreement between the theoretical analysis and the numerical simulations of the MCAL equation for the Ml.

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