Eur. Phys. J. Plus (2019) 134: 598
https://doi.org/10.1140/epjp/i2019-12992-3

Regular Article

Solitary wavelike solutions in nonlinear dynamics of damped DNA systems

¹ Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
² African Center of Excellence in Information and Communication Technologies, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
³ International Center for Complex Systems, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaounde, Cameroon
⁴ Complex Systems, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon
⁵ Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

^* e-mail: okalyjoseph@yahoo.fr

Received: 14 April 2019
Accepted: 10 September 2019
Published online: 4 December 2019

Abstract

The internal mobility of the DNA molecule, in a weakly damped medium, is studied. Inspired by the microscopic Peyrard-Bishop-Dauxois model, a zigzag model, which considers longitudinal and transverse vibrations of base pairs is used. The damped limit is considered and the whole system is shown to be governed by a dissipative nonlinear Schrödinger equation. The linear stability analysis of a plane wave solution is thereafter performed. The oscillations and open states of the DNA duplex are also addressed, where two hyperbolic functions are used to construct DNA bubbles in the form of bright- and kink-type soliton solutions. The confirmation of analytical predictions is verified through direct numerical experiments. There are good accuracy and good agreement between the quantitative and qualitative influence of damping forces on the width and amplitude of the moving soliton. Such relevant results could be used to predict the generation of moving bubbles along the DNA molecule, and to explain energy transfer and localization processes during the fundamental processes of DNA replication and transcription.