Modulation instability and pattern formation in damped molecular systems

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Subtitle: Modulation instability and pattern formation in damped molecular systems

Publisher: American Scientific Publishers

Publication year: 2009

Volume number: 6

Issue number: 3

Start page: 583

End page: 592

Number of pages: 10

ISSN: 1546-1955

URL: https://doi.org/10.1166/jctn.2009.1076

Languages: English-United States (EN-US)

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Abstract

It is shown that, in the weak amplitude and slow time limits, the dynamics of a damped one-dimensional 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 (MI) criterion. We show that, if the wave amplitude exceeds a certain threshold value, the initial solution breaks into pulse train. Energy localization via MI 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 MI.

Keywords

DAMPING; MODIFIED COMPLEX ABLOWITZ-LADIK EQUATION; MODULATIONAL INSTABILITY

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