Abstract
This article is devoted to the study of the Englander model in a potential field. In the model, nuclides are represented as a pendulum connected by a common thread. Based on the Englander model, the sine-Gordon equation, which describes nonlinear systems, has been investigated. New nonlinear models such as the Peyrard-Bishop model, the Poland-Scheraga model, the Yakushevich model, and the Scott model have been considered. Using the Englander model, the functionality of the DNA molecule is explained and treated as a graphical structure. The structural changes in the Englander model are based on kink and anti-kink. Analytical and numerical values of the kink characteristics are calculated. It is shown how topological aspects are utilized in nonlinear models of the DNA molecule. The complex dynamics of DNA and its topological defects are described. Modeling of the dynamic process during transcription and replication by applying an equation to DNA is considered. Using the DNA parameters, solutions to the equation are obtained in the form of kink and anti-kink. The energy density of kink and antikink is found. Density curves and surfaces of kinks and anti-kinks are constructed. Separation of variables methods are used to find solutions in differential equations. 2D and 3D plots of kink and anti-kink interactions are obtained using Python software.