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The inviscid limit for the complex Ginzburg–Landau equation

Journal of Mathematical Analysis and Applications, 2003
We study the inviscid limit of the complex Ginzburg–Landau equation. We observe that the solutions for the complex Ginzburg–Landau equation converge to the corresponding solutions for the nonlinear Schrödinger equation. We give its convergence rate.
Shuji Machihara
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Dynamic Bifurcation of the Ginzburg--Landau Equation

SIAM Journal on Applied Dynamical Systems, 2004
Summary: 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 ...
Tian Ma, Jungho Park, Shouhong Wang
openaire   +1 more source

On the Ginzburg-Landau Wave Equation

Bulletin of the London Mathematical Society, 1990
Consider the initial value problem of the Ginzburg-Landau wave equation with a general power self-interaction term: \[ (*)\quad \phi_ t=(1+i\alpha)\Delta \phi +(1+i\beta)\phi -(1+i\gamma)| \phi |^{\mu -1}\phi,\quad x\in {\mathbb{R}}^ n,\quad t>0, \] \[ \phi (x,0)=\phi_ 0(x),\quad x\in {\mathbb{R}}^ n, \] where \(\phi\) is a complex scalar function ...
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A Bifurcation Analysis for the Ginzburg-Landau Equation

Archive for Rational Mechanics and Analysis, 1998
The authors consider the following boundary-value problem for the Ginzburg-Landau equation \[ \begin{aligned}-\Delta u={1\over\varepsilon^2} u_\varepsilon(1-|u_\varepsilon|^2)\quad &\text{in }B,\\ u_\varepsilon(z)= z^d\quad &\text{on }\partial B,\end{aligned}\tag{1} \] where \(B\) is the unit ball of \(\mathbb{R}^2\), \(d\in\mathbb{N}^*\) and ...
Comte, Myriam, Mironescu, Petru
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Global Existence of Solutions to the Derivative 2D Ginzburg–Landau Equation

Journal of Mathematical Analysis and Applications, 2000
In this paper we study a complex derivative Ginzburg–Landau equation with two spatial variables (2D). We obtain sufficient conditions for the existence and uniqueness of global solutions for the initial boundary value problem of the derivative 2D ...
Li, Yongsheng, Guo, Boling
exaly   +2 more sources

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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On the Burgers-Ginzburg-Landau equations

Communications in Nonlinear Science and Numerical Simulation, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Boling, Huang, Haiyang
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Ginzburg–Landau equations for superconductivity

2023
Abstract 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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