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.

arXiv commentLaTeX, 19 pages, 2 figures

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Cited by in corpus (8)

• Continuous Limit of Discrete Systems with Long-Range Interaction
• An implicit midpoint difference scheme for the fractional Ginzburg-Landau equation
• Map of Discrete System into Continuous
• Fractional Derivative as Fractional Power of Derivative
• Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory
• A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
• Kinetic dominance and psi series in the Hamilton-Jacobi formulation of inflaton models
• A three-level linearized difference scheme for the coupled nonlinear fractional Ginzburg-Landau equation