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

Nickolay Korabel and George M. Zaslavsky

Physica A: Statistical Mechanics and its Applications, 2007, vol. 378, issue 2, 223-237

Abstract: Discrete nonlinear Schrödinger (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/l1+α with fractional α<2 and l as a distance between oscillators. This model is called αDNLS. It exhibits competition between the nonlinearity and a level of correlation between interacting far-distanced oscillators, that is defined by the value of α. We consider transition to chaos in this system as a function of α and nonlinearity. It is shown that decreasing of α 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 αDNLS can be correspondingly extended to the FNLS.

Keywords: Long-range interaction; Discrete NLS; Fractional equations; Spatio–temporal chaos (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:378:y:2007:i:2:p:223-237

DOI: 10.1016/j.physa.2006.10.041

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