Modulated waves in the DNA double helix with finite stacking enthalpy interaction

We report on properties of modulational instability and the generation of soliton-like excitations in DNA nucleotides. Taking the finite stacking enthalpy model of DNA dynamics as an example, we show that the original difference-differential equation for the DNA dynamics can be reduced to a modified discrete nonlinear Schrödinger equation. We derive the modulational instability criterion in this case. Numerical simulations show the validity of the analytical approach with the generation of wave packets provided that the wavenumbers fall in the instability domain. The impact of the finite stacking energy is investigated and we show that low values of the finite stacking enthalpy contribute to highly enhance the amplitude of localized excitations and the density of energy as well.