Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity

Journal article

Authors / Editors

Tabi, Condrad

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Publication Details

Author list: Tabi CB, Mohamadou A, Kofane TC

Publisher: AIMS Press

Place: SPRINGFIELD

Publication year: 2008

Journal: Mathematical Biosciences and Engineering (1547-1063)

Journal acronym: MATH BIOSCI ENG

Volume number: 5

Issue number: 1

Start page: 205

End page: 216

Number of pages: 12

ISSN: 1547-1063

eISSN: 1551-0018

Languages: English-Great Britain (EN-GB)

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Abstract

The study of solitary wave solutions is of prime significance for nonlinear physical systems. The Peyrard-Bishop model for DNA dynamics is generalized specifically to include the difference among bases pairs and viscosity. The small amplitude dynamics of the model is studied analytically and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Exact solutions of the obtained wave equation are obtained by the mean of the extended Jacobian elliptic function approach. These amplitude solutions are made of bubble solitons. The propagation of a soliton-like excitation in a DNA is then investigated through numerical integration of the motion equations. We show that discreteness can drastically change the soliton shape. The impact of viscosity as well as elasticity on DNA dynamic is also presented. The profile of solitary wave structures as well as the energy which is initially evenly distributed over the lattice are displayed for some fixed parameters.

Keywords

bubble soliton, density energy, discrete complex Ginzburg-Landau equation, DNA Dynamics, Jacobian elliptic functions

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