#### Filter Results:

#### Publication Year

1993

2008

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

- G M Zaslavsky, R Z Sagdeev, D A Usikov, A A Chernikov Frontmatter
- 2005

and in Path Integrals and their Applications in Quantum S set of real numbers is said to be relatively Statistical and Solid State Physics, edited by G. P. dense if there exists a number L< 00 such that any inter-Papadopoulous and G. T. Devreese (Plenum, New York, val on the real axis of length L contains at least one 1977) 0 member of E. 12We define the… (More)

- N Laskin, G Zaslavsky
- 2008

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. Classical case is treated in the framework of the well-known Frenkel-Kontorova chain model. Qunatum dynamics is considered follow to Davydov's approach to molecular excitons. In the continuum limit the problem is reduced to… (More)

We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-range powerwise interaction. The corresponding term in dynamical equations is proportional to 1//n-m/alpha+1. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order alpha,… (More)

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order ao2 is dissipation.… (More)

We derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of… (More)

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 α, when 0 < α < 2. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both… (More)

Chaotic ray dynamics in deep sea propagation models is considered using the approaches developed in the theory of dynamical chaos. It has been demonstrated that the mechanism of emergence of ray chaos due to overlapping of nonlinear ray-medium resonances should play an important role in long range sound propagation. Analytical estimations, supported by… (More)

- H Weitzner, G M Zaslavsky
- 2002

We present two observations related to the application of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE. The transition of the solution from normal to anomalous transport is demonstrated and the dominant role of the power… (More)