scholarly journals ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations

1980 ◽  
Vol 72 (3) ◽  
pp. 277-292 ◽  
Author(s):  
Clifford Henry Taubes
Keyword(s):  
Ginzburg Landau ◽  
First Order ◽  
Vortex Solutions ◽  
Ginzburg Landau Equations

scholarly journals Periodic solutions to the self-dual Ginzburg–Landau equations

1999 ◽  
Vol 10 (3) ◽  
pp. 285-295
Author(s):  
Y. ALMOG
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Critical Case ◽  
Topological Invariant ◽  
The Self ◽  
Ginzburg Landau ◽  
First Order ◽  
Vortex Solution ◽  
Ginzburg Landau Equations ◽  
Existence Of Periodic Solutions

The structure of periodic solutions to the Ginzburg–Landau equations in R2 is studied in the critical case, when the equations may be reduced to the first-order Bogomolnyi equations. We prove the existence of periodic solutions when the area of the fundamental cell is greater than 4πM, M being the overall order of the vortices within the fundamental cell (the topological invariant). For smaller fundamental cell areas, it is shown that no periodic solution exists. It is then proved that as the boundaries of the fundamental cell go to infinity, the periodic solutions tend to Taubes' arbitrary N-vortex solution.

scholarly journals A theory of giant vortices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Alexander A. Penin ◽  
Quinten Weller
Keyword(s):  
Asymptotic Expansion ◽  
Analytic Form ◽  
Scalar Fields ◽  
Winding Number ◽  
Asymptotic Results ◽  
Convergence Region ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Neutral Scalar ◽  
Vortex Solutions

Abstract We elaborate a theory of giant vortices [1] based on an asymptotic expansion in inverse powers of their winding number n. The theory is applied to the analysis of vortex solutions in the abelian Higgs (Ginzburg-Landau) model. Specific properties of the giant vortices for charged and neutral scalar fields as well as different integrable limits of the scalar self-coupling are discussed. Asymptotic results and the finite-n corrections to the vortex solutions are derived in analytic form and the convergence region of the expansion is determined.

Virial theorem and Abrikosov’s solution of the Ginzburg-Landau equations

1991 ◽  
Vol 44 (14) ◽  
pp. 7704-7707 ◽  
Author(s):  
U. Klein ◽  
B. Pöttinger
Keyword(s):  
Virial Theorem ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

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