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Books on the topic 'Ginzburg-Landau equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Bethuel, Fabrice. Ginzburg-Landau vortices. Birkhäuser, 1994.

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2

Herbert, Geoffrey M. Stability analysis of the Fisher and Landau-Ginzburg equations. typescript, 1995.

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3

Duong, Giao Ky, and Nejla Nouaili. Construction of Blowup Solutions for the Complex Ginzburg-Landau Equation with Critical Parameters. American Mathematical Society, 2023.

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4

Hélein, Frédéric, Fabrice Bethuel, and Haïm Brezis. Ginzburg-Landau Vortices. Birkhäuser, 2017.

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5

Helein, Frederic, Haim Brezis, and Fabrice Bethuel. Ginzburg-Landau Vortices. Birkhauser Verlag, 2012.

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6

Ginzburg-Landau Vortices. World Scientific Publishing Co Pte Ltd, 2005.

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7

Ginzburg-Landau Vortices. World Scientific Publishing Co Pte Ltd, 2005.

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8

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the

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9

Tang, Q., and K. H. Hoffmann. Ginzburg-Landau Phase Transition Theory and Superconductivity. Birkhäuser Boston, 2012.

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10

(Editor), Haim Brezis, and Daqian Li (Editor), eds. Ginzburg-landau Vortices (Series in Contemporary Applied Mathematics). World Scientific Publishing Company, 2005.

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11

Analysis of Ginzburg-Landau Vortices (Progress in Nonlinear Differential Equations & Their Applications). Birkhauser Verlag AG, 2000.

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12

Zeitlin, Vladimir. Resonant Wave Interactions and Resonant Excitation of Wave-guide Modes. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0012.

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The idea of resonant nonlinear interactions of waves, and of resonant wave triads, is first explained using the example of Rossby waves, and then used to highlight a mechanism of excitation of wave-guide modes, by impinging free waves at the oceanic shelf, and at the equator. Physics and mathematics of the mechanism, which is related to the phenomena of parametric resonance and wave modulation, are explained in detail in both cases. The resulting modulation equations, of Ginzburg–Landau or nonlinear Schrodinger type, are obtained by multi-scale asymptotic expansions and elimination of resonanc

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13

Vortices in the Magnetic Ginzburg-Landau Model (Progress in Nonlinear Differential Equations and Their Applications). Birkhäuser Boston, 2006.

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14

Vortices in the Magnetic Ginzburg-Landau Model (Progress in Nonlinear Differential Equations and Their Applications Book 70). Birkhäuser, 2008.

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15

Ginzburg-Landau Phase Transition Theory and Superconductivity (International Series of Numerical Mathematics, V. 134.). Birkhauser (Architectural), 2000.

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16

Pacard, Frank, and Tristan Riviere. Linear and Nonlinear Aspects of Vortices: The Ginzburg-Landau Model (Progress in Nonlinear Differential Equations and Their Applications). Birkhäuser Boston, 2000.

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