Formation of localized structures in the Peyrard-Bishop-Dauxois model

We explore in detail the properties of modulational instability (MI) and the generation of soliton-like excitations in DNA nucleotides. Based on the Peyrard-Bishop-Dauxois (PBD) model of DNA dynamics, which takes into account the interaction with neighbors in the structure, we derive through the semidiscrete approximation a modified discrete nonlinear Schrödinger (MDNLS) equation. From this equation, we predict the condition for the propagation of modulated waves through the system. To verify the validity of these results we have carried out numerical simulations of the PBD model and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the MDNLS equation. In the simulations we have found that a train of pulses are generated when the lattice is subjected to MI, in agreement with the analytical results obtained in an MDNLS equation. Also, the effects of the harmonic longitudinal and helicoidal constants on the dynamics of the system are notably pointed out. The process of energy localization from a nonsoliton initial condition is also explored.