Transition to chaos in discrete nonlinear Schrodinger equation with long-range interaction

Discrete nonlinear Schrodinger (DNLS) equation describes a chain of oscillators with nearest-neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to 1/l(l+alpha) with fractional alpha < 2 and l as a distance between oscillators. This model is called alpha DNLS. It exhibits competition between the nonlinearity and a level of correlation between interacting far-distanced oscillators, that is defined by the value of alpha. We consider transition to chaos in this system as a function of alpha and nonlinearity. It is shown that decreasing of alpha with respect to nonlinearity stabilize the system. Connection of the model to the fractional generalization of the NLS (called FNLS) in the long-wave approximation is also discussed and some of the results obtained for alpha DNLS can be correspondingly extended to the FNLS. Published by Elsevier B.V.