Energy localization in the Peyrard-Bishop DNA model

We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup on a long time scale. We use a localization criterion based on the information entropy and verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter (mu>2.25) (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is mu=6.3). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.