Dynamic behavior of dark and bright solitons with analytical solutions, together with other soliton forms in the double-chain DNA Model

This study explores the double-chain DNA model, which plays a crucial role in the preservation and transmission of genetic information in biosystems. The model is made of two strings that reflect DNA’s intertwined polynucleotide bands. The polynucleotide chains are joined by an elastic membrane that simulates hydrogen bonding within each base pair. The modified Sardar sub-equation method and the extended Jacobi elliptic function expansion methodology are used to obtain analytical soliton solutions containing bright solitons, dark solitons, W-shaped solitons, kink solitons, multi-solitons, multi-lumps, and traveling waves. The 3D and 2D visualizations provide information on longitudinal and transverse movements inside the DNA helix. The visual assessment of some of the results revealed the existence of solitary waves in DNA strands. This study represents an important advance in our understanding of DNA motions. It focuses on the important concepts of human genetic data synthesis and transfer. The originality of this work depends on the fact that it gives new findings for the presented equation that have not been previously studied. The findings of this study are expected to have important applications in soliton theory, plasma physics, optical fibers, physical engineering, and nonlinear dynamics.