On the location of defects in stationary solutions of the Ginzburg-Landau equation in $\textbf {R}^2$
Authors:
P. C. Fife and L. A. Peletier
Journal:
Quart. Appl. Math. 54 (1996), 85-104
MSC:
Primary 35Q55
DOI:
https://doi.org/10.1090/qam/1373840
MathSciNet review:
MR1373840
Full-text PDF Free Access
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Additional Information
F. Bethuel, H. Brezis, and F. Hélein, Limite singulière pour la minimisation de fonctionelles du type Ginzburg-Landau, C. R. Acad. Sci. Paris 314, 891–895 (1992)
F. Bethuel, H. Brezis, and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994
F. Bethuel, H. Brezis, and F. Hélein, Tourbillons de Ginzburg-Landau et énergie renormalisée, C. R. Acad. Sci. Paris 317, 165–171 (1993)
S. Chandrasekhar and G. S. Ranganath, Adv. Phys. 35, 507 (1986)
D. S. Cohen, J. C. Neu, and R. Rosales, Rotating spiral wave solutions of reaction-diffusion equations, SIAM J. Appl. Math. 35, 536–547 (1978)
R. J. Donnelley, Quantized Vortices in Helium II, Cambridge University Press, Cambridge, 1991
J. M. Greenberg, Spiral waves for $\lambda - \omega$ systems, SIAM J. Appl. Math. 39, 301–309 (1980)
V. L. Ginzburg and L. D. Landau, Statistical Physics, Pergamon Press, 1980
P. Hagan, Spiral waves in reaction-diffusion equations, SIAM J. Appl. Math. 42, 762–786 (1982)
J. M. Kosterlitz and D. J. Thouless, Two-dimensional physics, in Progress in Low Temperature Physics VII B (Ed. D. F. Brewer), North-Holland, 1978
Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer-Verlag, New York, 1984
J. C. Neu, Vortices in complex scalar fields, Physica D 43, 385–406 (1990)
L. M. Pismen and J. D. Rodriguez, Mobility of singularities in the dissipative Ginzburg-Landau equation, Phys. Rev. A 42, 2471–2474 (1990)
L. M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model, Physica D 47, 353–360 (1991)
L. M. Pismen and J. Rubinstein, Dynamics of defects
J. Rubinstein, Self-induced motion of line defects, Quart. Appl. Math. 49, 1–10 (1991)
J. Rubinstein, P. Sternberg, and J. B. Keller, Reaction-diffusion processes and evolution to harmonic maps, SIAM J. Appl. Math. 49, 1722–1733 (1989)
F. Bethuel, H. Brezis, and F. Hélein, Limite singulière pour la minimisation de fonctionelles du type Ginzburg-Landau, C. R. Acad. Sci. Paris 314, 891–895 (1992)
F. Bethuel, H. Brezis, and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, Boston, 1994
F. Bethuel, H. Brezis, and F. Hélein, Tourbillons de Ginzburg-Landau et énergie renormalisée, C. R. Acad. Sci. Paris 317, 165–171 (1993)
S. Chandrasekhar and G. S. Ranganath, Adv. Phys. 35, 507 (1986)
D. S. Cohen, J. C. Neu, and R. Rosales, Rotating spiral wave solutions of reaction-diffusion equations, SIAM J. Appl. Math. 35, 536–547 (1978)
R. J. Donnelley, Quantized Vortices in Helium II, Cambridge University Press, Cambridge, 1991
J. M. Greenberg, Spiral waves for $\lambda - \omega$ systems, SIAM J. Appl. Math. 39, 301–309 (1980)
V. L. Ginzburg and L. D. Landau, Statistical Physics, Pergamon Press, 1980
P. Hagan, Spiral waves in reaction-diffusion equations, SIAM J. Appl. Math. 42, 762–786 (1982)
J. M. Kosterlitz and D. J. Thouless, Two-dimensional physics, in Progress in Low Temperature Physics VII B (Ed. D. F. Brewer), North-Holland, 1978
Y. Kuramoto, Chemical Oscillations, Waves and Turbulence, Springer-Verlag, New York, 1984
J. C. Neu, Vortices in complex scalar fields, Physica D 43, 385–406 (1990)
L. M. Pismen and J. D. Rodriguez, Mobility of singularities in the dissipative Ginzburg-Landau equation, Phys. Rev. A 42, 2471–2474 (1990)
L. M. Pismen and J. Rubinstein, Motion of vortex lines in the Ginzburg-Landau model, Physica D 47, 353–360 (1991)
L. M. Pismen and J. Rubinstein, Dynamics of defects
J. Rubinstein, Self-induced motion of line defects, Quart. Appl. Math. 49, 1–10 (1991)
J. Rubinstein, P. Sternberg, and J. B. Keller, Reaction-diffusion processes and evolution to harmonic maps, SIAM J. Appl. Math. 49, 1722–1733 (1989)
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© Copyright 1996
American Mathematical Society
