Fractional Ginzburg–Landau equation for fractal media
نویسندگان
چکیده
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 the fractional Ginzburg–Landau equation or nonlinear Schrödinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied. r 2005 Elsevier B.V. All rights reserved. PACS: 03.40. t; 05.45.Df; 47.53.+n
منابع مشابه
Exact solutions of the 2D Ginzburg-Landau equation by the first integral method
The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.
متن کاملFractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
Equations built on fractional derivatives prove to be a powerful tool in the description of complex systems when the effects of singularity, fractal supports, and long-range dependence play a role. In this paper, we advocate an application of the fractional derivative formalism to a fairly general class of critical phenomena when the organization of the system near the phase transition point is...
متن کاملSome new exact traveling wave solutions one dimensional modified complex Ginzburg- Landau equation
In this paper, we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method, homogeneous balance method, extended F-expansion method. By using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...
متن کاملPsi-series solution of fractional Ginzburg–Landau equation
One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...
متن کاملThe Solution of Fractional Nonlinear Ginzburg–landau Equation with Weak Initial Data
In this paper, we study the solution of the fractional nonlinear Ginzburg-Landau(FNGL) equation with weak initial data in the weighted Lebesgue spaces. The existence of a solution to this equation is proved by the contraction-mapping principle.
متن کامل