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Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation. (English) Zbl 0575.76055

The bifurcation structure and asymptotic dynamics of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation are investigated analytically and numerically. All solutions spring from unstable periodic modulations of a uniform wavetrain. Asymptotic states include limit cycles, two-tori, and chaotic attractors. Lyapunov exponents for some chaotic motions are obtained. These show the solution strange attractors to have a fractal dimension slightly greater than 3.

MSC:

76F99 Turbulence
76M99 Basic methods in fluid mechanics
76E99 Hydrodynamic stability
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