Coupled oscillators with power-law interaction and their fractional dynamics analogues
Nickolay Korabel, George M. Zaslavsky, Vasily E. Tarasov
Abstract
The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order α, when 0<α<2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.
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