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Generalized Ginzburg–Landau equations in high dimensions

Calculus of Variations and Partial Differential Equations, 2017
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Ge, Yuxin, Sandier, Etienne, Zhang, Peng
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Vortices in Ginzburg-Landau equations

1998
Summary: 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, 2014
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Small energy solutions to the Ginzburg–Landau equation

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
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F. Bethuel   +2 more
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The Ginzburg–Landau equation for interfacial instabilities

Physics of Fluids A: Fluid Dynamics, 1992
A 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, 1993
A 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, 1996
The 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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On the Ginzburg-Landau equations

Archive for Rational Mechanics and Analysis, 1964
Carroll, Robert W., Glick, A. J.
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