Fractional Ginzburg–Landau equation for fractal media
Fractional Ginzburg–Landau equation for fractal media
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DOI：
10.1016/j.physa.2005.02.047
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发表时间：
2005-08
影响因子：
3.3
通讯作者：
V. E. Tarasov;G. Zaslavsky
中科院分区：
文献类型：
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作者：
V. E. Tarasov;G. Zaslavsky
我们从分形介质的变分欧拉-拉格朗日方程中推导出金兹堡-朗道方程的分数阶推广。为了描述分形介质，我们使用分数积分作为分形积分的近似值。考虑了分形介质的Ginzburg-Landau方程的一些简单解，并提出了分数式Ginzburg-Landau方程或具有分数阶导数的非线性薛定谔方程的不同形式。阿格拉瓦尔变分原理及其推广已得到应用。
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.