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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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Ginzburg–Landau equations for superconductivity
2023Abstract This chapter presents the Ginzburg-Landau equations, which are the core of the phenomenological theory of superconductivity of Ginzburg and Landau. First it follows the historical path to describe the formalism of F. and H. London and derive their equations.
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Nonlocal Ginzburg-Landau Equations
Communications in Theoretical Physics, 1990Real time Gor'kov equations and the accompanying electric current expression in terms of the retarded Green's functions are established at finite temperatures with the aid of the Closed-Time-Path-Green's-Function formalism. The fluctuation-dissipation theorem then helps us to obtain nonlocal G-L equations near Tc which reduces to the conventional G-L ...
Hong-hua Xu, Chien-hua Tsai
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On the Burgers-Ginzburg-Landau equations
Communications in Nonlinear Science and Numerical Simulation, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Boling, Huang, Haiyang
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The Ginzburg-Landau Equation in ℂ
2000In this chapter we begin the study of Ginzburg-Landau vortices. To begin with, we define u 1, the radially symmetric solution of the Ginzburg-Landau equation in all ℂ, and also L 1, the linearized Ginzburg-Landau operator about u 1. Next we carry out a careful study of all possible asymptotic behaviors of a solution of the homogeneous equation L 1 E ...
Frank Pacard, Tristan Rivière
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Low-Dimensional Models of the Ginzburg--Landau Equation
SIAM Journal on Applied Mathematics, 2001The author considers homogeneous Neumann boundary conditions and Dirichlet boundary conditions for a system of complex Ginzburg-Landau equations. By Fourier-Galerkin procedure, the equations are cast into a finite-dimensional dynamical description. A nonlinear variational principle is used to extracted principal interaction patterns from the system.
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Stationary Ginzburg–Landau Equations
2020Starting with this Chapter, we will consecutively introduce the basic framework which will eventually allow us to present the derivation of time-dependent Ginzburg–Landau equations.
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On the Ginzburg-Landau equations
Archive for Rational Mechanics and Analysis, 1964Carroll, Robert W., Glick, A. J.
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On the validity of the Ginzburg-Landau equation
Journal of Nonlinear Science, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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