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Coupled oscillators with power-law interaction and their fractional dynamics analogues

Nickolay Korabel·George M. Zaslavsky·Vasily E. Tarasov
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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 $\alpha$, when $0<\alpha<2$. 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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Nickolay Korabel, George M. Zaslavsky, Vasily E. Tarasov. 2006-03-28. Coupled oscillators with power-law interaction and their fractional dynamics analogues. https://doi.org/10.1016/j.cnsns.2006.03.015

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