Soliton dynamics and stability analysis of a double-chain DNA model with various chaos detection tools

This investigation employs an analytical approach, specifically the extended Jacobian elliptic expansion function method, to investigate the soliton dynamics of the double-chain model of DNA. Using this scheme, the kink wave, anti-kink wave, dark soliton, bright soliton, breather wave with a singularity, multiple breather waves with a singularity, and periodic wave are obtained. Next, the stability analysis of the governing equation is examined using linear stability theory. Moreover, stability assessment of the achieved outcomes is provided by the Hamiltonian approach. This study also employs various tools to explore the chaotic nature of the stated nonlinear problem, including strange attractors, recurrence plots, bifurcation plots, and fractal dimensions. The results demonstrate that our employed scheme is more efficient, more dependable, and easier to implement than any other scheme employed in the existing literature.