Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field

J. M. Gonçalves Ribeiro

Annales de l'I.H.P. Physique théorique (1991)

  • Volume: 54, Issue: 4, page 403-433
  • ISSN: 0246-0211

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Gonçalves Ribeiro, J. M.. "Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field." Annales de l'I.H.P. Physique théorique 54.4 (1991): 403-433. <http://eudml.org/doc/76536>.

@article{GonçalvesRibeiro1991,
author = {Gonçalves Ribeiro, J. M.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {instability properties of solutions; variational problem},
language = {eng},
number = {4},
pages = {403-433},
publisher = {Gauthier-Villars},
title = {Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field},
url = {http://eudml.org/doc/76536},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Gonçalves Ribeiro, J. M.
TI - Instability of symmetric stationary states for some nonlinear Schrödinger equations with an external magnetic field
JO - Annales de l'I.H.P. Physique théorique
PY - 1991
PB - Gauthier-Villars
VL - 54
IS - 4
SP - 403
EP - 433
LA - eng
KW - instability properties of solutions; variational problem
UR - http://eudml.org/doc/76536
ER -

References

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  1. [1] H. Berestycki a4cnd T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon nonlinéaires, C.R. Acad. Sci. Paris, T. 293, 1981, pp. 489-492. Zbl0492.35010MR646873
  2. [2] H. Berestycki and P.L. Lions, Nonlinear Scalar Field Equations. I, Arch. Rat. Mech. Anal., Vol. 82, 1983, pp. 313-345. Zbl0533.35029MR695535
  3. [3] P. Blanchard, J. Stubbe and L. Vasquez, On the Stability of Solitary Waves for Classical Scalar Fields, Ann. Inst. Henri-Poincaré, Phys. Théor., Vol. 47, 1987, pp. 309-336. Zbl0649.35076MR921309
  4. [4] T. Cazenave, An Introduction to Nonlinear Schödinger Equations, Textos de Métodos Matemáticos. No. 22, I.M.U.F.R.J., Rio de Janeiro, 1989. 
  5. [5] T. Cazenave and M. Esteban, On the Stability of Stationary States for Nonlinear Schrödinger Equations with an External Magnetic Field, Mat. Apl. Comp., Vol. 7, 1988, pp. 155-168. Zbl0681.35011MR994761
  6. [6] T. Cazenave and P.L. Lions, Orbital Stability of Standing Waves for some Nonlinear Schrödinger Equations, Comm. Math. Phys., Vol. 85, 1982, pp. 549-561. Zbl0513.35007MR677997
  7. [7] M. Esteban and P.L. Lions, Stationnary Solutions of Nonlinear Schrödinger Equations with an External Magnetic Field. In Partial Differential Equations and the Calculus of Variations, F. COLOMBINI et al. Eds., Birkhäuser, Boston, 1989, pp. 401-409. Zbl0702.35067MR1034014
  8. [8] Gonçalves Ribeiro, Finite Time Blow-up for Some Nonlinear Schrödinger Equations with an External Magnetic Field (to appear). Zbl0734.35127
  9. [9] M. Grillakis, J. Shatah and W.A. Strauss, Stability Theory of Solitary Waves in the Presence of Symmetry. I, J. Funct. Anal., Vol. 74, 1987, pp. 160-197. Zbl0656.35122MR901236
  10. [10] P. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986. Zbl0588.22001MR836734
  11. [11] J. Shatah, Stable Standing Waves of Nonlinear Klein-Gordon Equations, Comm. Math. Phys., Vol. 91, 1983, pp. 313-327. Zbl0539.35067MR723756
  12. [12] J. Shatah, Unstable Ground States of Nonlinear Klein-Gordon Equations, Trans. Am. Math. Soc., Vol. 290, 1985, pp. 701-710. Zbl0617.35072MR792821
  13. [13] J. Shatah and W.A. Strauss, Instability of Nonlinear Bound States, Comm. Math. Phys., Vol. 100, 1985, pp. 173-190. Zbl0603.35007MR804458
  14. [14] W.A. Strauss, Existence of Solitary Waves in Higher Dimensions, Comm. Math. Phys., Vol. 55, 1977, pp. 149-162. Zbl0356.35028MR454365
  15. [15] J. Stubbe, Linear Stability Theory of Solitary Waves arising from Hamiltonian Systems with Symmetry, Portug. Math., Vol. 46, 1989, pp. 17-32. Zbl0687.35088MR996398
  16. [16] M. Weinstein, Liapounov Stability of Ground States of Nonlinear Dispersive Evolution Equations, Comm. Pure Appl. Math., Vol. 39, 1968, pp. 51-67. Zbl0594.35005MR820338

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