Modulational instability of charge transport in the Peyrard–Bishop–Holstein model

Abstract

We report on modulational instability (MI) on a DNA charge transfer model known as thePeyrard–Bishop–Holstein (PBH) model. In the continuum approximation, the systemreduces to a modified Klein–Gordon–Schrödinger (mKGS) system through which linearstability analysis is performed. This model shows some possibilities for the MI region andthe study is carried out for some values of the nearest-neighbor transfer integral.Numerical simulations are then performed, which confirm analytical predictionsand give rise to localized structure formation. We show how the spreading ofcharge deeply depends on the value of the charge–lattice-vibrational coupling.