Influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model

Abstract

We report in this paper the influence of the discrete lattice spacing on the formation of intrinsic localized structures in the Salerno model. Through the linear stability analysis, appearance criterions of the modulation instability (MI) are derived. We show via the growth rate that, the discrete lattice spacing and the nonlinearity term can affect significantly the formation of instability zones. We find that for large values of the discrete lattice spacing, the MI is developed to increase the number instability zones whereas for very low values of this parameter, the MI growth rate is arisen up to enlarge the bandwidth. The theoretical findings have been numerically tested via the discrete spatial Fourier transform method and the direct simulations, and have been found to be in full agreement with the analytical prediction. Moreover, it has been revealed that a higher modulation index can dramatically modify the shape and the amplitude of the modulated waves.