Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice

Through the multiple scale expansion, we show that the dynamics of modulated waves in a two-component helicoidal one-dimensional model is governed by the nonlinear Schrödinger (NLS) equation. We study the occurrence of patterns formation in such a system. The impact of the helicoidal coupling is also studied which reveals that high values of the helicoidal coupling constant contribute to regulate information and charge transport throughout the two-chain model. This is made possible due to the superposition of optical and acoustic modes. In addition, the model is used to investigate internal dynamics of DNA. It is shown that the opening of the double helix of the DNA itself is controlled by the resonance mode, where the unzipping of the double helix has been illustrated by numerical simulations. Furthermore, the shape of the eyelike shape previously observed in experiments of thermal denaturation of DNA is numerically obtained.