Twist-radial model for DNA opening with the power-law dependence of long-range interaction

This letter examines soliton dynamics in a twist-radial DNA model featuring power-law long-range interactions (LRIs) and competing nonlocal couplings, capturing the intricate interplay between radial and torsional degrees of freedom. Employing a multiple-scale expansion, we derive an amplitude equation in the form of the nonlinear Schrödinger equation, for which exact solutions are known and discussed in detail. Analytical and numerical analyses reveal nonlinear regimes characterized by localized excitations, radial breathers, and breathing kinks in the torsional domain, whose stability is markedly enhanced by long-range effects. These findings underscore that nonlinearity and nonlocal interactions are essential for DNA's efficient storage and transmission of energy, offering deeper insight into the physical principles governing its dynamic behavior.