Stationary modulated-amplitude waves in the 1-D complex Ginzburg-Landau equation

2002/07/31 by Yueheng Lan, Nicolas Garnier, Lan, Yueheng +4
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum optics and atomic interactions #nlin.CD #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0208001

29 pages, 4 figures

arxiv created 2002/07/31 · arxiv updated 2009/11/30

Abstract

We reformulate the one-dimensional complex Ginzburg-Landau equation as a fourth order ordinary differential equation in order to find stationary spatially-periodic solutions. Using this formalism, we prove the existence and stability of stationary modulated-amplitude wave solutions. Approximate analytic expressions and a comparison with numerics are given.

Citations

• Pattern formation outside of equilibrium

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