Formation of localized structures in the Peyrard-Bishop-Dauxois model

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

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We explore in detail the properties of modulational instability (MI) and the generation of soliton-like excitations in DNA nucleotides. Based on the Peyrard-Bishop-Dauxois (PBD) model of DNA dynamics, which takes into account the interaction with neighbors in the structure, we derive through the semidiscrete approximation a modified discrete nonlinear Schrödinger (MDNLS) equation. From this equation, we predict the condition for the propagation of modulated waves through the system. To verify the validity of these results we have carried out numerical simulations of the PBD model and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the MDNLS equation. In the simulations we have found that a train of pulses are generated when the lattice is subjected to MI, in agreement with the analytical results obtained in an MDNLS equation. Also, the effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. The process of energy localization from a nonsoliton initial condition is also explored.

Original languageEnglish
Article number415104
JournalJournal of Physics Condensed Matter
Volume20
Issue number41
DOIs
Publication statusPublished - Oct 15 2008

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Nonlinear equations
nonlinear equations
DNA
deoxyribonucleic acid
nucleotides
Nucleotides
Solitons
simulation
solitary waves
harmonics
propagation
Computer simulation
pulses
approximation
excitation
interactions
energy

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Condensed Matter Physics

Cite this

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abstract = "We explore in detail the properties of modulational instability (MI) and the generation of soliton-like excitations in DNA nucleotides. Based on the Peyrard-Bishop-Dauxois (PBD) model of DNA dynamics, which takes into account the interaction with neighbors in the structure, we derive through the semidiscrete approximation a modified discrete nonlinear Schr{\"o}dinger (MDNLS) equation. From this equation, we predict the condition for the propagation of modulated waves through the system. To verify the validity of these results we have carried out numerical simulations of the PBD model and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the MDNLS equation. In the simulations we have found that a train of pulses are generated when the lattice is subjected to MI, in agreement with the analytical results obtained in an MDNLS equation. Also, the effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. The process of energy localization from a nonsoliton initial condition is also explored.",
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Formation of localized structures in the Peyrard-Bishop-Dauxois model. / Tabi, Conrad B.; Mohamadou, Alidou; Kofané, Timoléon C.

In: Journal of Physics Condensed Matter, Vol. 20, No. 41, 415104, 15.10.2008.

Research output: Contribution to journalArticle

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