Map of Discrete System into Continuous

Details Map of Discrete System into Continuous Map of Discrete System into Continuous

2007-11-16

arxiv.org/abs/0711.2612v1

Journal of Mathematical Physics 47 (2006) 092901

Physics

Mathematical Physics

32 pages, LaTeX

Scientific paper

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the continuous limit is discussed. The one-dimensional systems of coupled oscillators for this type of long-range interactions are considered. The discrete equations of motion are mapped into the continuum equation with the Riesz fractional derivative.

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