  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.
