Fractional dynamics of systems with long-range interaction |
| |
| Institution: | 1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia;2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA;3. Department of Physics, New York University, 2–4 Washington Place, New York, NY 10003, USA;1. Institut de Physique Théorique, CEA-Saclay, F-91191, Gif-sur-Yvette cedex, France;2. Deutsches Elektronensynchrotron DESY, Platanenallee 6, D-15738 Zeuthen, Germany;3. Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX, United Kingdom |
| |
| Abstract: | We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/∣n ? m∣α+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 α, when 0 < α < 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: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
