Fractional Ginzburg-Landau equation for fractal media

被引：166
|
作者：
Tarasov, VE [1 ]
Zaslavsky, GM
机构：
[1] Moscow MV Lomonosov State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119992, Russia
[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA
[3] NYU, Dept Phys, New York, NY 10003 USA
来源：
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2005年 / 354卷
基金：
美国国家科学基金会;
关键词：
fractional equation; fractional derivatives and integrals fractal medium; Ginzburg-Landau equation;
D O I：
10.1016/j.physa.2005.02.047
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
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 Schrodinger equation with fractional derivatives are presented. The Agrawal variational principle and its generalization have been applied. (c) 2005 Elsevier B.V. All rights reserved.
引用
收藏
页码：249 / 261
页数：13
相关论文
共 50 条
  • [1] Well-posedness and dynamics for the fractional Ginzburg-Landau equation
    Pu, Xueke
    Guo, Boling
    APPLICABLE ANALYSIS, 2013, 92 (02) : 318 - 334
  • [2] An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation
    He, Dongdong
    Pan, Kejia
    NUMERICAL ALGORITHMS, 2018, 79 (03) : 899 - 925
  • [3] An unconditionally stable linearized difference scheme for the fractional Ginzburg-Landau equation
    Dongdong He
    Kejia Pan
    Numerical Algorithms, 2018, 79 : 899 - 925
  • [4] Analytical solution of the Ginzburg-Landau equation
    Wellot, Yanick Alain Servais
    Nkaya, Gires Dimitri
    EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, 15 (04): : 1750 - 1759
  • [5] Remarks on an Equation of the Ginzburg-Landau Type
    Wang, Bei
    FILOMAT, 2019, 33 (18) : 5913 - 5917
  • [6] Dynamic bifurcation of the Ginzburg-Landau equation
    Ma, T
    Park, J
    Wang, SH
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2004, 3 (04): : 620 - 635
  • [7] Time-space fractional stochastic Ginzburg-Landau equation driven by fractional Brownian motion
    Xu, Pengfei
    Zou, Guang-an
    Huang, Jianhua
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 78 (12) : 3790 - 3806
  • [8] An Insensitizing Control Problem for the Ginzburg-Landau Equation
    Santos, Mauricio Cardoso
    Tanaka, Thiago Yukio
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 183 (02) : 440 - 470
  • [9] A remark on multiplicity of solutions for the Ginzburg-Landau equation
    Zhou, F
    Zhou, Q
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1999, 16 (02): : 255 - 267
  • [10] Spatiotempora　lcomplexity　of　the　Cubic　Ginzburg－Landau　Equation
    Boling GUO
    Communications in Nonlinear Science & Numerical Simulation, 1996, (04) : 14 - 19
12345