Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions

The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schr\"odinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.