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

Abstract

We explore in detail the properties of modulational instability (MI) and the generation ofsoliton-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 thestructure, we derive through the semidiscrete approximation a modified discrete nonlinearSchrödinger (MDNLS) equation. From this equation, we predict the condition for thepropagation of modulated waves through the system. To verify the validity of these resultswe have carried out numerical simulations of the PBD model and the initial conditions inthe form of planar waves whose modulated amplitudes are given by the examples studied inthe MDNLS equation. In the simulations we have found that a train of pulses aregenerated when the lattice is subjected to MI, in agreement with the analytical resultsobtained in an MDNLS equation. Also, the effects of the harmonic longitudinal andhelicoidal constants on the dynamics of the system are notably pointed out. Theprocess of energy localization from a nonsoliton initial condition is also explored.