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Psi-Series Solution of Fractional Ginzburg-Landau Equation

Vasily E. Tarasov
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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 $α/(1-s)$ near the singularity.

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Vasily E. Tarasov. 2006-06-28. Psi-Series Solution of Fractional Ginzburg-Landau Equation. https://doi.org/10.1088/0305-4470%2F39%2F26%2F008

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