Quantitative analysis of soliton molecules in the (2 + 1)-Dimensional Double-Chain DNA system with beta derivative: Novel insights from an analytical approach

This study employs the unified method to analyze fractional-order DNA systems and constructs various soliton solutions. These include kink, anti-kink, singular, singular-periodic, periodic, and hybrid solitons in different parameter regimes. Graphical depictions of these solutions demonstrate the system’s spatiotemporal dynamics, revealing dual wave behaviors and the influence of physical parameters on soliton formation. The results indicate that the dual behavior of kink-antikink solitons may offer insights into the formation of an open-state configuration within the DNA double helix. Specifically, the amplitude of the anti-kink wave profile increases as the distance between the DNA strands grows, and the soliton profile shifts with varying stiffness and cross-sectional area. Additionally, the oscillatory wave remains unaffected by stiffness and area in terms of amplitude, though its profile undergoes shifts under varying conditions. This study provides a mathematical framework that bridges applied mathematics and molecular biology, enabling the exploration of DNA dynamics.