Dynamics on the attractor for the complex Ginzburg-Landau equation

Technical Report · Mon Aug 01 04:00:00 EDT 1994

DOI:https://doi.org/10.2172/10174640· OSTI ID:10174640

Takac, P ^[1]

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1. Vanderbilt Univ., Nashville, TN (United States). Dept. of Mathematics

We present a numerical study of the large-time asymptotic behavior of solutions to the one-dimensional complex Ginzburg-Landau equation with periodic boundary conditions. Our parameters belong to the Benjamin-Feir unstable region. Our solutions start near a pure-mode rotating wave that is stable under sideband perturbations for the Reynolds number R ranging over an interval (R{sub sub},R{sub sup}). We find sub- and super-critical bifurcations from this stable rotating wave to a stable 2-torus as the parameter R is decreased or increased past the critical value R{sub sub} or R{sub sup}. As R > R{sub sup} further increases, we observe a variety of dynamical phenomena, such as a local attractor consisting of three unstable manifolds of periodic orbits or 2-tori cyclically connected by manifolds of connection orbits. We compare our numerical simulations to both rigorous mathematical results and experimental observations for binary fluid mixtures.

• Research Organization: Argonne National Lab., IL (United States)
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 10174640
• Report Number(s): ANL/MCS/PP--75712; ON: DE94016902
• Country of Publication: United States
• Language: English

Related Subjects

665411
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS
990200
ASYMPTOTIC SOLUTIONS
ATTRACTORS
BASIC SUPERCONDUCTIVITY STUDIES
BIFURCATION
BINARY MIXTURES
BOUNDARY CONDITIONS
GINZBURG-LANDAU THEORY
MATHEMATICS AND COMPUTERS
NUMERICAL SOLUTION
REYNOLDS NUMBER
SUPERCONDUCTIVITY