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On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation
Abstract and Applied Analysis, 2014 We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation (1/2⩽α⩽1) in any spatial dimension n⩾1 with rough initial data.
Chunyan Huang
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Solitons and Jacobi Elliptic Function Solutions to the Complex Ginzburg–Landau Equation
Frontiers in Physics, 2020 The complex Ginzburg–Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified ...
Kamyar Hosseini +6 more
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Homogenization of a Ginzburg–Landau functional
Comptes Rendus. Mathématique, 2004 We consider a nonlinear homogenization problem for a Ginzburg–Landau functional with a (positive or negative) surface energy term describing a nematic liquid crystal with inclusions. Assuming that sizes and distances between inclusions are of the same order ɛ , we obtain a limiting functional
Berlyand, Leonid +2 more
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On Moving Ginzburg-Landau Vortices [PDF]
Communications in Analysis and Geometry, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Curl-free Ginzburg–Landau vortices [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 1999 For certain nonlinear elliptic PDE problems in two dimensions, the classical isoperimetric inequality produces a sharp inequality that violates a Pohozaev identity except for radial symmetric, decreasing solutions. A generalized version of this technique is used here to prove radial symmetry of curl-free Ginzburg-Landau vortices.
Chanillo, Sagun +1 more
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Finsler geometry in anisotropic superconductivity: a Ginzburg-Landau approach [PDF]
Open Communications in Nonlinear Mathematical PhysicsWe present a rigorous generalization of the classical Ginzburg--Landau model to smooth, compact Finsler manifolds without boundary. This framework provides a natural analytic setting for describing anisotropic superconductivity within Finsler geometry ...
Y. Alipour Fakhri
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Microscopic derivation of Ginzburg-Landau theories for hierarchical quantum Hall states
SciPost Physics, 2020 We propose a Ginzburg-Landau theory for a large and important part of the abelian quantum Hall hierarchy, including the prominently observed Jain sequences.
Yoran Tournois, Maria Hermanns, Thors Hans Hansson
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The energy of Ginzburg–Landau vortices
European Journal of Applied Mathematics, 2002 We consider the Ginzburg–Landau equation in dimension two. We introduce a key notion of the vortex (interaction) energy. It is defined by minimizing the renormalized Ginzburg–Landau (free) energy functional over functions with a given set of zeros of given local indices.
Ovchinnikov, Y. N., Sigal, I. M.
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Thermal Fluctuations of the superconducting order parameter in the Ginzburg-Landau theory [PDF]
, 2022 This thesis briefly explains the role of thermal fluctuations in the Ginzburg-Landau theory of superconductivity. We firstly explain the phenomenological aspects of superconductivity, then we describe the Ginzburg-Landau theory of superconductivity, with
Zuliani, Davide
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Ginzburg–Landau equations and their generalizations
Indagationes Mathematicae, 2023 The Ginzburg-Landau equations were proposed in the superconductivity theory to describe mathematically the intermediate state of superconductors in which the normal conductivity is mixed with the superconductivity. It was understood later on that these equations play an important role also in various problems of mathematical physics.
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