Effects of next-nearest-neighbor interactions on discrete multibreathers corresponding to Davydov model with saturable nonlinearities

Abstract

The influence of next-nearest-neighbor interactions (next-NNI) of dipole–dipole type is analyzed in Davydov model with saturable nonlinearities. We analytically study the regions of discrete modulational instability (MI) of plane carrier waves and it appears that this region decreases as the number of nearest neighbors, m, increases. We also show via the instability growth rate (gain) that when m increases, bandwidth of instability decreases. Otherwise, it is noted that the saturation also has an antagonistic effect on the gain. Numerical simulations indicate that the presence of next-NNI induced downward corrections of the time of onset of MI. After having sought Discrete Soliton (DS) and Discrete Multihump soliton (DMHS) numerically with m=1; 2; 3, the next-nearest neighbor dependence of the width and height of these solutions is discussed. A study of mobility is achieved and it results that next-NNI increase the speed of DMHS. Furthermore, the collisions of two DMHS are performed and it emerges mainly that next-NNI lead to the formation of large stationary solitons.