Instability of standing waves for the generalized Davey-Stewartson system

Masahito Ohta

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 62, Issue: 1, page 69-80
  • ISSN: 0246-0211

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Ohta, Masahito. "Instability of standing waves for the generalized Davey-Stewartson system." Annales de l'I.H.P. Physique théorique 62.1 (1995): 69-80. <http://eudml.org/doc/76669>.

@article{Ohta1995,
author = {Ohta, Masahito},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {ground states; criterion of instability},
language = {eng},
number = {1},
pages = {69-80},
publisher = {Gauthier-Villars},
title = {Instability of standing waves for the generalized Davey-Stewartson system},
url = {http://eudml.org/doc/76669},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Ohta, Masahito
TI - Instability of standing waves for the generalized Davey-Stewartson system
JO - Annales de l'I.H.P. Physique théorique
PY - 1995
PB - Gauthier-Villars
VL - 62
IS - 1
SP - 69
EP - 80
LA - eng
KW - ground states; criterion of instability
UR - http://eudml.org/doc/76669
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, Vol. 293, 1981, pp. 489-492. Zbl0492.35010MR646873
  2. [2] 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
  3. [3] R. Cipolatti, On the existence of standing waves for a Davey-Stewartson system, Comm. P.D.E., Vol. 17, 1992, pp. 967-988. Zbl0762.35109MR1177301
  4. [4] R. Cipolatti, On the instability of ground states for a Davey-Stewartson system, Ann. Inst. H. Poincaré, Phys. Théor., Vol. 58, 1993, pp. 85-104. Zbl0784.35106MR1208793
  5. [5] A. Davey and K. Stewartson, On three-dimensional packets of surfae waves, Proc. R. Soc., A., Vol. 338, 1974, pp. 101-110. Zbl0282.76008MR349126
  6. [6] 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
  7. [7] 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, 1991, pp. 403-433 Zbl0741.35080MR1128864
  8. [8] M. Ohta, Stability of standing waves for the generalized Davey-Stewartson system, J. Dyn. Diff. Eq. (to appear). Zbl0805.35098MR1280142
  9. [9] J. Shatah and W.A. Strauss, Instability of nonlinear bound states, Comm. Math. Phys., Vol. 100, 1985, pp. 173-190. Zbl0603.35007MR804458
  10. [10] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys., Vol. 87, 1983, pp. 567-576. Zbl0527.35023MR691044

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