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Fractional Ginzburg-Landau Equation
2010Complex Ginzburg-Landau equation (Aranson and Kramer, 2002) is one of the most-studied equations in physics. This equation describes a lot of phenomena including nonlinear waves, second-order phase transitions, and superconductivity. We note that the Ginzburg-Landau equation can be used to describe the evolution of amplitudes of unstable modes for any ...
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Dynamic Bifurcation of the Ginzburg--Landau Equation
SIAM Journal on Applied Dynamical Systems, 2004Summary: We study in this article the bifurcation and stability of the solutions of the Ginzburg-Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as \(\lambda\) crosses the first critical value of the linear problem ...
Ma, Tian, Park, Jungho, Wang, Shouhong
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Synchronization in nonidentical complex Ginzburg-Landau equations
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006A cross-correlation coefficient of complex fields has been investigated for diagnosing spatiotemporal synchronization behavior of coupled complex fields. We have also generalized the subsystem synchronization way established in low-dimensional systems to one- and two-dimensional Ginzburg-Landau equations.
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Generalized Ginzburg–Landau equations in high dimensions
Calculus of Variations and Partial Differential Equations, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ge, Yuxin, Sandier, Etienne, Zhang, Peng
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Vortices in Ginzburg-Landau equations
1998Summary: GL models were first introduced by V. Ginzburg and L. Landau around \(1950\) in order to describe superconductivity. Similar models appeared soon after for various phenomena: Bose condensation, superfluidity, non linear optics. A common property of these models is the major role of topological defects, termed in our context vortices.
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Adiabatic Limit for Hyperbolic Ginzburg–Landau Equations
Journal of Mathematical Sciences, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Small energy solutions to the Ginzburg–Landau equation
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Bethuel +2 more
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The Ginzburg–Landau equation for interfacial instabilities
Physics of Fluids A: Fluid Dynamics, 1992A coherent method for pursuing a numerical multiple scales analysis of an interface problem is presented. Finding numerical boundary conditions for the homogeneous adjoint problem and evaluation of surface terms in the inhomogeneous solvability criteria is reduced to one singular value decomposition. The method is applied to derive the complex Ginzburg–
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Laser Ginzburg-Landau equation and laser hydrodynamics
Physical Review A, 1993A laser Ginzburg-Landau equation with fourth- and higher-order diffusion terms is derived from the Maxwell-Bloch equations describing a laser. It is shown that the higher-order diffusion terms in the laser Ginzburg-Landau equation are crucial for the transverse structure formation.
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The Validity of Generalized Ginzburg-Landau Equations
Mathematical Methods in the Applied Sciences, 1996The work is devoted to a rigorous derivation of the Ginzburg-Landau (GL) equations as an asymptotic limit of nonlinear ultraparabolic equations describing systems of hydrodynamic origin, in which a stationary homogeneous state becomes unstable, at a critical value of a control parameter, against spatial perturbations with a finite wavelength.
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