Semi-discrete breather in a helicoidal DNA double chain-model |
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Affiliation: | 1. Centre for Undergraduate Studies, University of the Punjab, Lahore 54590, Pakistan;2. Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan;3. Department of Mathematics, Minhaj University, Lahore, Pakistan;1. Bilecik Seyh Edebali University, Bozuyuk Vocational School, Bilecik, Turkey;2. Eskişehir Osmangazi University, Art–Science Faculty, Department of Mathematics–Computer, Eskişehir, Turkey |
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Abstract: | The nonlinear dynamics of DNA molecular chain is studied for longitudinal and transversal motions through a new discrete helicoidal zigzag model with four degrees of freedom. We take into account the Stokes and hydrodynamical viscous forces. In the semi-discrete approximation, we show that the coupled nonlinear partial differential equations for the longitudinal and transversal out-of-phase motions can be reduced to the nonlinear Schrödinger equation with complex coefficients, allowing analytical breather soliton solution. We found analytically as well as numerically that increasing the damping constant reduces the amplitude and increases the width of the soliton. When the zigzag angle decreases, the height of the soliton increases, but its width remains constant. The linear stability analysis of the system is performed. The growth rate of the instability and the instability regions are discussed as the functions of damping constant, zigzag angle and system parameters. |
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Keywords: | Zigzag DNA double helix model Damping forces Longitudinal and transversal out-of-phase motions Modulational instability Soliton |
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