On the instability of ground states for a Davey-Stewartson system

Rolci Cipolatti

Annales de l'I.H.P. Physique théorique (1993)

  • Volume: 58, Issue: 1, page 85-104
  • ISSN: 0246-0211

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Cipolatti, Rolci. "On the instability of ground states for a Davey-Stewartson system." Annales de l'I.H.P. Physique théorique 58.1 (1993): 85-104. <http://eudml.org/doc/76599>.

@article{Cipolatti1993,
author = {Cipolatti, Rolci},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {standing wave; ground states; unstable set},
language = {eng},
number = {1},
pages = {85-104},
publisher = {Gauthier-Villars},
title = {On the instability of ground states for a Davey-Stewartson system},
url = {http://eudml.org/doc/76599},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Cipolatti, Rolci
TI - On the instability of ground states for a Davey-Stewartson system
JO - Annales de l'I.H.P. Physique théorique
PY - 1993
PB - Gauthier-Villars
VL - 58
IS - 1
SP - 85
EP - 104
LA - eng
KW - standing wave; ground states; unstable set
UR - http://eudml.org/doc/76599
ER -

References

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  1. [1] H. Berestycki and T. Cazenave, Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaires, C. R. Acad. Sci., Paris, T. 293, Series I, 1981, pp. 489-492. Zbl0492.35010MR646873
  2. [2] T. Cazenave, Stability and Instability of Stationary States in Nonlinear Schrödinger Equations, Contributions to nonlinear partial differential equations I, Research Notes in Math., Vol. 89, Pitman, London, 1983. Zbl0528.35008MR730802
  3. [3] T. Cazenave. An Introduction to Nonlinear Schrödinger Equations, Textos de Métodos Matemáticos, Vol. 22, I.M.U.F.R.J., Rio de Janeiro, 1989. 
  4. [4] T. Cazenave and P.-L. Lions, Orbital Stability of Standing Waves for Nonlinear Schrödinger Equations, Commun. Math. Phys., Vol. 85, 1982, pp. 549-561. Zbl0513.35007MR677997
  5. [5] R. Cipolatti, On the Existence of Standing Waves for a Davey-Stewartson System, Commun. in P.D.E. (to appear). Zbl0762.35109MR1177301
  6. [6] A. Davey and K. Stewartson, On Three-Dimensional Packets of Surface Waves, Proc. R. Soc. A., Vol. 338, 1974, pp. 101-110. Zbl0282.76008MR349126
  7. [7] J.-M. Ghidaglia and J.-C. Saut, On the Initial Value Problem for the Davey-Stewartson Systems, Nonlinearity, Vol. 3, 1990, pp. 475-506. Zbl0727.35111MR1054584
  8. [8] J.M. Gonçalves Ribeiro, Instability of Symmetric Stationary States for Some Nonlinear Schrödinger Equations with an External Magnetic Field, Ann. Inst. H. Poincaré; Phys. Théor., Vol. 54, No. 4, 1992, pp. 403-433. Zbl0741.35080MR1128864
  9. [9] M. Grillakis, J. Shatah and W.A. Strauss, Stability Theory of Solitary Waves in Presence of Symmetry I, J. Functional Analysis, Vol. 74, 1987, pp. 160-197. Zbl0656.35122MR901236
  10. [10] J. Shatah and W.A. Strauss, Instability of Nonlinear Bound States, Commun Math. Phys., Vol. 100, 1985, pp. 173-190. Zbl0603.35007MR804458
  11. [11] M.I. Weinstein, Nonlinear Schrödinger Equations and Sharp Interpolation Estimates, Comm. Math. Physics, Vol. 87, 1983, pp. 567-576. Zbl0527.35023MR691044

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