Fractional dynamics of systems with long-range interaction
نویسندگان
چکیده
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction defined by a term proportional to 1/jn mj. Continuous medium equation for this system can be obtained in the socalled 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 a, when 0 < a < 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. 2006 Elsevier B.V. All rights reserved. PACS: 05.45. a; 45.05.+x; 45.50. j
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