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Coupled oscillators with power-law interaction and their fractional dynamics analogues
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 , when . 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.Comment: 16 pages, 5 figure
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