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Research in the Commonwealth of Independent States on Superconducting Materials: Current State and Prospects. [PDF]

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Tolendiuly S   +5 more
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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
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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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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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Small energy solutions to the Ginzburg–Landau equation

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Bethuel   +2 more
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Onset of chaos in the generalized Ginzburg-Landau equation

Physical Review A, 1990
Study of chaos in the generalized Ginzburg-Landau equation (GLE) $$ {\text{iu}}_{\text{t}} + {\text{u}}_{{\text{xx}}} + 2\left| {\text{u}} \right|^{\text{2}} {\text{u}} = {\text{i}} \in _1 {\text{u}} - {\text{i}} \in _3 \left| {\text{u}} \right|^2 {\text{u}} + {\text{i}} \in _2 u_{{\text{xx}}} $$ (1) is a subject of great current interest ...
, Malomed, , Nepomnyashchy
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