Solitary waves and bifurcation analysis in a double-chain DNA model

This study investigated the double-chain deoxyribonucleic acid (DNA) model that is at the heart of conservation and transmission of genetic information in biological systems. The model consists of a pair of strands that simulates DNA's intertwined chains of polynucleotides. These chains are bonded together by an elastic membrane that simulates hydrogen bonds between base pairs. To analyze the nonlinear dynamics of this system, the modified extended direct algebraic method was employed to derive exact analytical solutions, including bright solitons, dark solitons, Jacobi elliptic (JE) solutions, and periodic structures. The 3D, 2D, and polar visualizations obtained show longitudinal and transverse dynamics of the DNA helix. Visual examination of the outcomes confirmed the presence of solitary waves on DNA strands. In addition to presenting some dynamical analyses, such as bifurcation and stability analyses. The current study is a significant landmark in the area of DNA dynamics, with emphasis on prominent aspects of genetic information synthesis and transmission. The novelty of this work lies in the derivation of new exact soliton solutions to the governing DNA model that, to the best of our knowledge, have not been previously reported. The findings are expected to contribute to a deeper understanding of DNA dynamics and may also have broader implications in soliton theory, nonlinear science, plasma physics, fiber optics, and physical engineering.