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.

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We study the nonlinear dynamics of the DNA double-helical chain using the Peyrard-Bishop-Dauxois (PBD) model. By using the Fourier series approach, we have found that the DNA dynamics in this case is governed by the modified discrete nonlinear Schrödinger (MDNLS) equation. Through the Jacobian elliptic function method, we investigate a set of exact solutions of this model. These solutions include the Jacobian periodic solution as well as bubble solitons. The stability of these solutions is also studied.

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