Psi-Series Solution of Fractional Ginzburg-Landau Equation

Abstract

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 $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha /(1-s)$ near the singularity.

LaTeX, 19 pages, 2 figures

References in corpus (6)

• Fractional Quantum Mechanics
• Fractional Hydrodynamic Equations for Fractal Media
• Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
• Fractional Liouville and BBGKI Equations
• Possible Experimental Test of Continuous Medium Model for Fractal Media
• Transport Equations from Liouville Equations for Fractional Systems

Cited by in corpus (2)

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