article · Physica Scripta
The nonlinear dynamics of the DNA double-helical chain can be examined mathematically using the Peyrard–Bishop–Dauxois model. Applying a Fourier series approach reveals that the motion and interactions within the chain are governed by the modified discrete nonlinear Schrödinger equation. Using the Jacobian elliptic function method, several exact solutions to this governing equation can be derived. These mathematical solutions feature both Jacobian periodic solutions and localised excitations known as bubble solitons. Alongside finding these exact solutions, the stability of both the periodic configurations and the bubble solitons is evaluated. This theoretical framework provides an analytical description of how wave patterns and localised openings behave along the double-helical structure.
Understanding the physical and mathematical mechanics of the DNA double helix offers fundamental insight into how mechanical energy travels along genetic material. Formulations such as bubble solitons help describe how the double helix temporarily opens, which is essential to genetic activity. Mathematical models clarify the precise conditions under which these stable structural patterns form and persist in biological chains.
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We study the nonlinear dynamics of the DNA double-helical chain using the Peyrard–Bishop–Dauxois (PBD) model. By using the Fourier series approach, we have found that the DNA dynamics in this case is governed by the modified discrete nonlinear Schrödinger (MDNLS) equation. Through the Jacobian elliptic function method, we investigate a set of exact solutions of this model. These solutions include the Jacobian periodic solution as well as bubble solitons. The stability of these solutions is also studied.
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DOI: 10.1088/0031-8949/77/4/045002
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