Unstable manifolds and Schrödinger dynamics of Ginzburg-Landau vortices

Nonlinearity

Volumn 15, Issue 5, 2002, Pages 1471-1488

  Lange, O ^a,b   Schroers, B J ^a  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b MAX PLANCK INSTITUTE FOR BIOPHYSICAL CHEMISTRY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042473258     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/5/307     Document Type: Article

References (19)

1. Bethuel F, Brézis H and Hélein F 1994 Ginzburg-Landau Vortices (Basle: Birkhäuser)
2. Ovchinnikov Y N and Sigal IM1997 Ginzburg-Landau equation: I. Static vortices Partial Differential Equations and their Applications (CRM Proc. and Lecture Notes) vol 12, ed P Greiner et al (Providence, RI: American Mathematical Society) pp 199-220
3. Neu J C 1990 Vortices in complex scalar fields Physica D 43 385-406
4. Neu J C 1990 Vortex dynamics of the non-linear wave equation Physica D 43 407-20
5. Lin F-H and Xin J X 1999 On the imcompressible fluid limit and the vortex motion law of the nonlinear Schrödinger equation Commun. Math Phys. 200 249-74
6. Lin F-H and Xin J X 1999 On the dynamical law of the Ginzburg-Landau vortices on the plane Commun. Pure Appl. Math. 52 1189-212
7. Colliander J E and Jerrard R L 1998 Vortex dynamics for the Ginzburg-Landau-Schrödinger equation Int. Math. Res. Notices 7 333-58
8. Ovchinnikov Y N and Sigal IM 1998 The Ginzburg-Landau equation: III. Vortex dynamics Nonlinearity 11 1277-94
9. Ovchinnikov Y N and Sigal I M 1998 Long-time behaviour of Ginzburg-Landau vortices Nonlinearity 11 1275-310
10. Manton N S 1988 Unstable manifolds and soliton dynamics Phys. Rev. Lett. 60 1916-9
11. 4 kinks-gradient flow and dynamics Nonlinearity 10 3-18
12. Papanicolaou N and Tomaras T N 1993 On the dynamics of vortices in a nonrelativistic Ginzburg-Landau model Phys. Lett. A 179 33
13. Dziarmaga J 1996 Dynamics of overlapping vortices in complex scalar fields Acta. Phys. Pol. B 27 1943-60
14. Ginibre J and Velo G 1996 The Cauchy problem in local spaces for the complex Ginzburg-Landau equation: 15. Compactness methods Physica D 95 191-228
15. Ginibre J and Velo G 1997 The Cauchy problem in local spaces for the complex Ginzburg-Landau equation: II. Contraction methods Commun. Math. Phys. 187 45-79
16. Manton N S 1997 First order vortex dynamics Ann. Phys. NY 256 114-31
17. Manton N S and Nasir S M 1999 Conservation laws in a first order dynamical system of vortices Nonlinearity 12 851-65
18. Atiyah M and Hitchin N 1988 Geometry and Dynamics of Monopoles (Princeton, NJ: Princeton University Press)
19. Stuart D 1994 Dynamics of abelian Higgs vortices in the near Bogomolny regime Commun. Math. Phys. 159 51-91