Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2013, Article ID 631089, 4 pages
http://dx.doi.org/10.1155/2013/631089
Research Article

Reduction of Chern-Simons-Schrödinger Systems in One Space Dimension

Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

Received 6 August 2013; Revised 31 October 2013; Accepted 31 October 2013

Academic Editor: Anjan Biswas

Copyright © 2013 Hyungjin Huh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. c. Kao, K. Lee, and T. Lee, “BPS domain wall solutions in self-dual Chern-Simons-Higgs systems,” Physical Review D, vol. 55, no. 10, pp. 6447–6453, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. Jackiw and S. Y. Pi, “Classical and quantal nonrelativistic Chern-Simons theory,” Physical Review D, vol. 42, no. 10, pp. 3500–3513, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. Leblanc, G. Lozano, and H. Min, “Extended superconformal Galilean symmetry in Chern-Simons matter systems,” Annals of Physics, vol. 219, no. 2, pp. 328–348, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. K. Nakamitsu and M. Tsutsumi, “The Cauchy problem for the coupled Maxwell-Schrödinger equations,” Journal of Mathematical Physics, vol. 27, no. 1, pp. 211–216, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Tsutsumi, “Global existence and uniqueness of energy solutions for the Maxwell-Schrödinger equations in one space dimension,” Hokkaido Mathematical Journal, vol. 24, no. 3, pp. 617–639, 1995. View at Google Scholar · View at MathSciNet
  6. L. Bergé, A. de Bouard, and J. C. Saut, “Blowing up time-dependent solutions of the planar, Chern-Simons gauged nonlinear Schrödinger equation,” Nonlinearity, vol. 8, no. 2, pp. 235–253, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. S. Demoulini, “Global existence for a nonlinear Schroedinger-Chern-Simons system on a surface,” Analyse Non Linéaire, vol. 24, no. 2, pp. 207–225, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. Demoulini and D. Stuart, “Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schrödinger system,” Communications in Mathematical Physics, vol. 290, no. 2, pp. 597–632, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Huh, “Energy solution to the Chern-Simons-Schrödinger equations,” Abstract and Applied Analysis, vol. 2013, Article ID 590653, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Huh, “Blow-up solutions of the Chern-Simons-Schrödinger equations,” Nonlinearity, vol. 22, no. 5, pp. 967–974, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Byeon, H. Huh, and J. Seok, “Standing waves of nonlinear Schrödinger equations with the gauge field,” Journal of Functional Analysis, vol. 263, no. 6, pp. 1575–1608, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Huh, “Standing waves of the Schrödinger equation coupled with the Chern-Simons gauge field,” Journal of Mathematical Physics, vol. 53, no. 6, Article ID 063702, 8 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. H. Huh, “Global energy solutions of Chern-Simons-Higgs equations in one space dimension,” Preprint. View at Google Scholar
  14. D. Cao, I. L. Chern, and J. C. Wei, “On ground state of spinor Bose-Einstein condensates,” Nonlinear Differential Equations and Applications, vol. 18, no. 4, pp. 427–445, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Journal of Experimental and Theoretical Physics, vol. 38, pp. 248–253, 1974. View at Google Scholar
  16. J. Yang, “Classification of the solitary waves in coupled nonlinear Schrödinger equations,” Physica D, vol. 108, no. 1-2, pp. 92–112, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. T. Wada, “Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger equations,” Journal of Functional Analysis, vol. 263, no. 1, pp. 1–24, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. H. Huh, “Remarks on Chern-Simons-Dirac equations in one space dimension,” Preprint. View at Google Scholar