Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

STANDING WAVE SOLUTIONS FOR THE PLANER CHERN-SIMONS GAUGED NONLINEAR SCHRODINGER EQUATION WITH AN EXTERNAL ELECTROMAGNETIC FIELD

  • Published : 2000.11.01
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Abstract

In this paper we construct a standing solitary wave solution with prescribed total electric charge to the planer Chern-Simons gauged nonlinear Schrodinger equation with an external electromagnetic field by using a variations method.

Keywords

References

  1. Duke Math. J. v.45 Schrodinger operators with magnetic fields. I. General interactions. Avron J.;Herbst I.;Simon B
  2. Chern-Simons gauged nonlinear Schrodinger equation, Nonlinearity v.8 Blowing up time dependent solutions of the planer Berge L.;de Bouard A.;Saut J.C.
  3. Comm. Partial Diff. Eq v.20 Existence and multiplicity results for some superlinear elliptic problems on Rⁿ Bartsch T.;Wang Z.-Q.
  4. Geometric and Fourier Anal. v.6 Conformal invariant systems of nonlinear PDE of Liouville type Chanillo, S.;Kiessing, M.K.-H.
  5. Duke Math. J. v.71 Qualitative properties of solutions to some nonlinear elliptic equations in R² Chen, W.;Li, C.
  6. Phys. Rev. D. v.44 Nonrelastivstic Chern-Simons vortex solitons in external magnetic field Ezawa Z.F.;Hotta M.;Iwasaki A
  7. Prog. Theo. Phys. Suppl. v.107 Anyon field theory and fractional quantum Hall statics.
  8. Grund. Math. Wiss. v.224 Elliptic Partial Differential Equations of Second Order, 2nd ed. Gilbarg D.;Trudinger N.S.
  9. J. Reine Angew. Math. v.404 Subsolution estimates and Harnack's inequality for Schrodinger operators Hinz, A.M.;Kalf, H.
  10. Math. Ana. v.294 Polynomial boundedness of eigenfunctions and the sepctrum of Schrodinger operators Hinz, A.M.;Stolz, G.
  11. Phys. REv. D. v.42 Classical and quantal nonrelativistic Chern-Simons theory Jackiw R.;Pi S.-Y.
  12. Phys. Rev. D. v.44 Time-dependent Chern-Simons solitons and their quantization
  13. Prog. Theo. Phys. Suppl. v.107 Self-Dual Chern-Simons Solitons
  14. Israel J. Math. v.13 Schrodinger operators with singular potentials Kato, T.
  15. Math. Z. v.224 Local boundeness and continuity for weak solutions of -(▽-ib)²u+ Vu=0 Kurata, K.
  16. Nonlinear Analysis v.41 Existence and semi-classical limit of the least energy solution to a nonlinear Schrodinger equation with electromagnetic fields
  17. J. London Math. Soc. An estimate on the Heat kernel of magnetic Schrodinger operators and uniformly elliptic operators with non-negative potentials
  18. Linear and Quasilinear Elliptic Equations Ladyzhenskaya, O.A.;Ural'tseva, N.N.
  19. Methods of Modern Mathematical Physics Ⅱ Reed M.;Simon B
  20. Ann. Inst. Fourier v.45 Lp estimates for Schrodinger operators with certain potentials Shen, Z.
  21. Indiana Univ. Math. J. v.45 Estimates in Lp for magnetic Schrodinger operators Shen, Z.
  22. Math. Z. v.131 Schrodinger operators with sigular magnetic vector potentials Simon, B.
  23. Fourier Integrals in Classical Analysis Sogge, C.D.