Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity
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Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde
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2.
Condensed Matter Physics Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala
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Received:
01 May 2007
Accepted:
29 June 2018
Published:
01 January 2008
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MSC :
37N25, 34J60, 34G34.
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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 vis-
cosity. The small amplitude dynamics of the model is studied analytically
and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Ex-
act 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.
Citation: Conrad Bertrand Tabi, Alidou Mohamadou, Timoleon Crepin Kofane. Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity[J]. Mathematical Biosciences and Engineering, 2008, 5(1): 205-216. doi: 10.3934/mbe.2008.5.205
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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 vis-
cosity. The small amplitude dynamics of the model is studied analytically
and reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Ex-
act 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.
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