Comprehensive error sensitivity analysis of nonlinear dynamics in DNA denaturation using the PB-DNA model

This study aims to explore the Peyrard–Bishop deoxyribonucleic acid (PB-DNA) dynamic model utilizing Heâ’s variational iteration (HVI) method, supported by the Khater III (Khat III) and improved Kudryashov (IKud) mathematical techniques. The PB-DNA model is essential for illustrating the nonlinear dynamics of DNA, a process vital for gene expression and DNA replication. This model shares similarities with other nonlinear evolution equations, such as the sine-Gordon and Klein–Gordon equations, which depict wave propagation in nonlinear media. Our approach involves employing the HVI method to obtain numerical solutions and leveraging the Khat III and IKud schemes to formulate exact solutions. This integrated strategy provides a thorough methodology for addressing the PB-DNA model, offering dual numerical and analytical insights. Key outcomes encompass the derivation of exact solutions unveiling the physical traits of DNA dynamics such as soliton and breather formations. These solutions pinpoint stability and instability zones within the PB-DNA molecule, furnishing precious insights for biological and medical research. The value of these results is in their capacity to deepen our comprehension of PB-DNA behavior across diverse conditions, potentially spurring progress in genetic engineering and medical therapies. A distinctive aspect of this study is the amalgamation of numerical and analytical methods, furnishing a sturdy solution to the PB-DNA model and presenting fresh viewpoints on PB-DNA dynamics. In summary, this research enriches the field of mathematical biology by delivering an in-depth analysis of the PB-DNA model through cutting-edge numerical and analytical methods. The findings shed light on the nonlinear dynamics of PB-DNA, holding implications for both theoretical and applied biological research. Moreover, the techniques employed in this paper may potentially be extended to the fractional version of the model, offering a promising avenue for young researchers to explore. Further investigation is required to establish the specific conditions for such an application, providing an opportunity for the scientific community to delve deeper into this exciting area of study.