Psi-Series Solution of Fractional Ginzburg-Landau Equation

Details Psi-Series Solution of Fractional Ginzburg-Landau Equation Psi-Series Solution of Fractional Ginzburg-Landau Equation

2006-06-28

arxiv.org/abs/nlin/0606070v1

Journal of Physics A 39 (2006) 8395-8407

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 19 pages, 2 figures

Scientific paper

10.1088/0305-4470/39/26/008

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.

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