Dynamics of perturbed wavetrain solutions to the Ginzburg-Landau equation

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5761670

Keefe, L R

The bifurcation structure of even, spatially periodic solutions to the time-dependent Ginzburg-Landau equation is investigated analytically and numerically. A rich variety of behavior, including limit cycles, two-tori, period-doubling sequences, and strange attractors are found to exist in the phase space of the solutions constructed from spatial Fourier modes. Beginning with unstable perturbations to the spatially homogeneous Stokes solution, changes in solution behavior are examined as the perturbing wavenumber q is varied in the range 0.6 to 1.3. Solution bifurcations as q changes are often found to be associated with symmetry making or breaking changes in the structure of attractors in phase space. Two distinct mirror image attractors are found to coexist for many values of q. Chaotic motion is found for two ranges of q Lyapunov exponents of the solutions and the Lyapunov dimension of the corresponding attractors are calculated for the larger of these regions. Poincare sections of the attractors within this chaotic range are consistent with the dimension calculation and also reveal a bifurcation structure within the chaos which broadly resembles that found in one-dimensional quadratic maps. The integrability of the Ginzburg-Landau equation is also examined. It is demonstrated that the equation does not possess the Painleve property, except for a special case of the coefficients which corresponds to the integrable non-linear Schroedinger (NLS) equation.

• Research Organization: University of Southern California, Los Angeles (USA)
• OSTI ID: 5761670
• Country of Publication: United States
• Language: English

Related Subjects

656101 -- Solid State Physics-- Superconductivity-- General Theory-- (-1987)
658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EQUATIONS
GINZBURG-LANDAU THEORY
INTEGRAL EQUATIONS
LIE GROUPS
LYAPUNOV METHOD
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
POINCARE GROUPS
SCHROEDINGER EQUATION
SPACE
STOKES PARAMETERS
SYMMETRY GROUPS
WAVE EQUATIONS