Modulation instability and pattern formation in damped molecular systems

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

Research output: Contribution to journalArticle

3 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 languageEnglish
Pages (from-to)583-592
Number of pages10
JournalJournal of Computational and Theoretical Nanoscience
Volume6
Issue number3
DOIs
Publication statusPublished - Mar 1 2009

Fingerprint

Pattern Formation
Damped
Modulation
modulation
Theoretical Analysis
Computer simulation
Modulational Instability
Linear Stability
Threshold Value
Exceed
Computer Simulation
computerized simulation
Numerical Simulation
thresholds
pulses
Energy
simulation
energy

All Science Journal Classification (ASJC) codes

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

Cite this

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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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Modulation instability and pattern formation in damped molecular systems. / Tabi, Conrad B.; Mohamadou, Alidou; Kofané, Timoléon C.

In: Journal of Computational and Theoretical Nanoscience, Vol. 6, No. 3, 01.03.2009, p. 583-592.

Research output: Contribution to journalArticle

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AU - Mohamadou, Alidou

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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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