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

  • Received: 01 May 2007 Accepted: 29 June 2018 Published: 01 January 2008
  • MSC : 37N25, 34J60, 34G34.

  • 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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  • 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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    © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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