Modulational instability and pattern formation on DNA dynamics with viscosity

We report on the analytical and numerical investigation of modulational instability in discrete nonlinear chains, taking the Peyrard-Bishop model of DNA dynamics as an example. It is shown that the original difference differential equation for the DNA dynamics can be reduced to the discrete complex Ginzburg-Landau 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 wave number fall in the instability domain. We also show that, modulational instability leads to spontaneous localization of energy in DNA molecule.