Modulational instability in DNA model with competing short- and long-range dispersive interactions

We study the modulational instability (MI) in the Peyrard-Bishop (PB) model of DNA dynamics, with short-range interaction, due to the stacking of base pairs, and long-range interaction, due to the finite dipole moment of the bonds within each base pair. Within the framework of the linear stability analysis, a critical value of the long-range coupling constant is found and, it is shown that, below this critical value, the system displays as the Klein-Gordon chain while, above the critical value, one can appreciate the influence of the dipole - dipole interactions. The study is supported by numerical analysis which confirms analytical predictions. Energy localization via MI is also investigated.