Fractional dynamics of systems with long-range interaction
Abstract
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power wise interaction defined by a term proportional to 1/|n-m|^{\alpha+1}. Continuous medium equation for this system can be obtained in the so-called infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of motion of the particles into a partial differential equation with the Riesz fractional derivative of order \alpha, when 0<\alpha<2. Few models of coupled oscillators are considered and their synchronized states and localized structures are discussed in details. Particularly, we discuss some solutions of time-dependent fractional Ginzburg-Landau (or nonlinear Schrodinger) equation.
Keywords
Cite
@article{arxiv.1107.5436,
title = {Fractional dynamics of systems with long-range interaction},
author = {Vasily E. Tarasov and George M. Zaslavsky},
journal= {arXiv preprint arXiv:1107.5436},
year = {2014}
}
Comments
arXiv admin note: substantial overlap with arXiv:nlin/0512013