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The time-dependent Ginzburg–Landau Maxwell equations
Nonlinear Analysis: Theory, Methods & Applications, 1999The paper considers the time dependent Ginzburg-Landau equations coupled with the Maxwell equations. A gradient flow is considered that is governed by a system in which the vector potential obeys parabolic equations, while the Maxwell equations are hyperbolic. The problem of Coulomb gauge invariance is also considered.
Tsutsumi, Masayoshi, Kasai, Hironori
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On the Ginzburg-Landau Wave Equation
Bulletin of the London Mathematical Society, 1990Consider 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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Rotating superconductors: Ginzburg-Landau equations
The European Physical Journal B - Condensed Matter, 2002Superconductors put into rotation develope a spontaneous internal magnetic field (the “London field”). In this paper Ginzburg Landau equations for order parameter, field, and current distributions for superconductors in rotation are derived. Two simple examples are discussed: the massive cylinder and the “Little and Parks geometry”: a thin film of ...
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Optical solitons with complex Ginzburg–Landau equation
Nonlinear Dynamics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mirzazadeh, Mohammad +9 more
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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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