Skyrmions in gross-pitaevskii functionals

Acta Mathematica Scientia

Volumn 29, Issue 3, 2009, Pages 751-776

  Lin, Fanghua ^a   Lin, Taichia ^b,c   Wei, Juncheng ^d  

^a NEW YORK UNIVERSITY   (United States)

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c Taida Institute of Mathematical Sciences (TIMS)   (Taiwan)

^d CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

35B25; 35B38; 35J60; Bose Einstein condensate; linked vortex rings; localized energy method; skyrmions

Indexed keywords

EID: 65449170532     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0252-9602(09)60069-2     Document Type: Article

References (22)

1. Anderson B.P., Haljan P.C., Regal C.A., Feder D.L., Collins L.A., Clark C.W., and Cornell E.A. Watching dark solitons decay into vortex rings in a Bose-Einstein condensate. Phys Rev Lett 86 (2001) 2926
2. Battye R.A., Cooper N.R., and Sutcliffe P.M. Stable skyrmions in two-component Bose-Einstein condensates. Phys Rev Lett 88 1-4 (2002) 080401
3. Babaev E., Faddeev L.D., and Niemi A.J. Hidden symmetry and knot solitons in a charged two-condensate Bose system. Phys Rev B 65 1-4 (2002) 100512
4. Chen X., Elliott C.M., and Qi T. Shooting method for vortex solutions of a complex-valued Ginzburg-Landau equation. Proc Roy Soc Edinburgh Sect A 124 (1994) 1075-1088
5. Esteban M. A direct variational approach to Skyrme's model for meson fields. Commun Math Phys 105 (1986) 571-591 Erratum to:
6. "A direct variational approach to Skyrme's model for meson fields". Comm Math Phys 251 1 (2004) 209-210
7. Hervé R.M., and Hervé M. Étude qualitative des solutions réelles d'une équation différentielle liée à l'équation de Ginzburg-Landau. Ann Inst H Poincaré Anal Non Linéaire 11 (1994) 427-440
8. Khawaja U.A., and Stoof H. Skyrmions in a ferromagnetic Bose-Einstein condensate. Nature 411 (2001) 918-920
9. Leggett A.J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev Mod Phys 73 (2001) 307-356
10. Lin F., and Yang Y. Existence of two-dimensional skyrmions via the concentration-compactness method. Comm Pure Appl Math 57 10 (2004) 1332-1351
11. Lin F., and Yang Y. Energy splitting, substantial inequality, and minimization for the Faddeev and Skyrme models. Comm Math Phys 269 1 (2007) 137-152
12. Lin T.C. The stability of the radial solution to the Ginzburg-Landau equation. Communication in Partial Differential Equations 22 3/4 (1997) 619-632
13. Frank P., and Tristan R. Linear and nonlinear aspects of vortices. The Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications 39 (2000), Birkhauser Boston, Inc, Boston, MA
14. Pitaevskii L., and Stringari S. Bose-Einstein Condensation (2003), Oxford University Press, Oxford
15. Rajaraman R. Solitons and Instantons (1989), North-Holland, Amsterdam
16. Ruostekoski J., and Anglin J.R. Creating vortex rings and three-dimensional skyrmions in Bose-Einstein condensates. Phys Rev Lett 86 1-4 (2001) 3934
17. Savage C.M., and Ruostekoski J. Energetically stable particlelike skyrmions in a trapped Bose-Einstein condensate. Phys Rev Lett 91 1-4 (2003) 010403
18. Skyrme T.H.R. A nonlinear-field theory. Proc R Soc London A 260 (1961) 127-138
19. Timmermans E. Phase separation of Bose-Einstein condensates. Phys Rev Lett 81 (1998) 5718-5721
20. Wei J. On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem. J Diff Eqns 129 (1996) 315-333
21. Wei J. On interior spike layer solutions for some sin gilar perturbation problems. Proc Royal Soc Edinburgh Section A 128 (1998) 849-974
22. Wei J. Existence and stability of spikes for the Gierer-Meinhardt system. In: Chipot M. (Ed). Handbook of Differential Equations: Stationary Partial Differential Equations Volume 5 (2008), Elsevier 487-585