Nonlinear Waves and Energy Localization in a Deoxyribonucleic Acid Double Chain

In this study, the dynamical behavior of a nonlinear DNA double-chain model, which depicts the double-helix formation of deoxyribonucleic acid (DNA), is analyzed. The proposed model is essential for the transfer of genetic information and the propagation of energy along biomolecular chains. The hydrogen bonds that connect the polynucleotide strands are depicted by modeling the two DNA chains as elastic rods joined by a flexible membrane, which gives rise to a nonlinear evolution equation that describes the transverse displacements occurring within the molecule. By employing the multivariate generalized exponential differential function method and the generalized Arnous technique, a number of wave solution is derived. The acquired solutions include bright solitons, kink soliton, lump soliton, W-shaped wave profiles and periodic wave patterns in suitable parametric values. The acquired wave structures are graphically represented using 3D surface graphs, density plots, and contour plotss, providing a clear visualization of the wave behaviors. These analytical results provide a theoretical framework for describing localized excitations and vibrational dynamics in DNA chains, offering analytical insight into internal nonlinear interactions within the biomolecular system. Moreover, we have studied the stability of the proposed model using linear stability analysis. The reported results extend existing studies on nonlinear DNA models and yield a more comprehensive insight into the processes of energy localization and transfer in biomolecular systems, while also showcasing the reliability and applicability of the solution methods utilized.