Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation

Details Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation Anomalous diffusion and anisotropic nonlinear Fokker-Planck equation

2006-02-22

arxiv.org/abs/nucl-th/0602061v1

Physica A342 (2004) 16-21

Physics

Nuclear Physics

Nuclear Theory

6 pages, tex file

Scientific paper

10.1016/j.physa.2004.04.054

We analyse a bidimensional nonlinear Fokker-Planck equation by considering an anisotropic case, whose diffusion coefficients are $D_x \propto |x|^{-\theta}$ and $D_y \propto |y|^{-\gamma}$ with $\theta, \gamma \in {\cal{R}}$. In this context, we also investigate two situations with the drift force $\vec{F}(\vec{r},t)=(-k_{x}x, -k_y y)$. The first one is characterized by $k_x/k_y=(2+\gamma)/(2+\theta)$ and the second is given by $k_{x}=k$ and $k_{y}=0$. In these cases, we can verify an anomalous behavior induced in different directions by the drift force applied. The found results are exact and exhibit, in terms of the $q$-exponentials, functions which emerge from the Tsallis formalism. The generalization for the $D$-dimensional case is discussed.

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