Kodai Mathematical Journal

Stability and instability of standing waves for one-dimensional nonlinear Schrödinger equations with double power nonlinearity

Masahito Ohta

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 18, Number 1 (1995), 68-74.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138043354

Digital Object Identifier
doi:10.2996/kmj/1138043354

Mathematical Reviews number (MathSciNet)
MR1317007

Zentralblatt MATH identifier
0868.35111

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B35: Stability

Citation

Ohta, Masahito. Stability and instability of standing waves for one-dimensional nonlinear Schrödinger equations with double power nonlinearity. Kodai Math. J. 18 (1995), no. 1, 68--74. doi:10.2996/kmj/1138043354. https://projecteuclid.org/euclid.kmj/1138043354


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References

  • [1] I. V. BARASHENKOV, A. D. GOCHEVA, V. G. MAKHANKOV AND I. V. PUZYNIN, Sta-bility of the soliton-like "bubbles", Physica D, 34 (1989), 240-254.
  • [2] H. BERESTYCKI AND T. CAZENAVE, Instabilite des etats stationnaires dans le equations de Schrdinger et de Klein-Gordon non lineaires, C. R. Acad. Sci. Paris, 293 (1981), 489-492.
  • [3] H. BERESTYCKI AND P. -L. LIONS, Nonlinear scalar field equations, I, Arch. Ra tional Mech. Anal., 82 (1983), 313-345.
  • [4] T. CAZENAVE AND P. -L. LIONS, Orbital stability of standing waves for som nonlinear Schrdinger equations, Comm. Math. Phys., 85 (1982), 549-561.
  • [5] T. CAZENAVE AND F. B. WEISSLER, The Cauchy problem for the nonlinea Schrodinger equation in H1, Manuscripta Math., 61 (1988), 477-494.
  • [6] J. GINIBRE AND G. VELO, On a class of nonlinear Schrdinger equations, I, J. Funct. Anal., 32 (1979), 1-32
  • [7] R. T. GLASSEY, On the blowing up of solutions to the Cauchy problem for non linear Schrodinger equations, J. Math. Phys., ]8 (1977), 1794-1797.
  • [8] M. GRILLAKIS, J. SHATAH AND W. A. STRAUSS, Stability theory of solitary wave in the presence of symmetry, I, J. Funct. Anal., 74 (1987), 160-197.
  • [9] I. D. ILIEV AND K. P. KIRCHEV, Stability and instability of solitary waves fo one-dimensional singular Schrdinger equations, Differential and Integral Equa-tions. 6 (1993), 685-703.
  • [10] T. KATO, On nonlinear Schrdinger equations, Ann. Inst. H. Poincare Phys Theor., 46 (1987), 113-129.
  • [11] K. KURATA AND T. OGAWA, Remarks on blowing-up of solutions for some non linear Schrodinger equations, Tokyo J. Math., 13 (1990), 399-419.
  • [12] J. SHATAH AND W. A. STRAUSS, Instability of nonlinear bound states, Comm Math. Phys., 100 (1985), 173-190.
  • [13] M. I. WEINSTEIN, Nonlinear Schrodinger equations and sharp interpolation esti mates, Comm. Math. Phys., 87 (1983), 567-576.