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Stable solitons of quadratic Ginzburg-Landau equations
Physical Review E, 2000We present a physical model based on coupled Ginzburg-Landau equations that supports stable temporal solitary-wave pulses. The system consists of two parallel-coupled cores, one having a quadratic nonlinearity, the other one being effectively linear. The former core is active, with bandwidth-limited amplification built into it, while the latter core ...
, Crasovan +4 more
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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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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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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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