Skip to main content
Log in

Stable standing waves of nonlinear Klein-Gordon equations

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear Klein-Gordon equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, D.L.T.: J. Math. Phys.12, 945–952 (1971)

    Google Scholar 

  2. Berestycki, H., Cazenave, T.: Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon, non linéaires. C. R. Acad. Sci.293A, 489–492 (1981)

    Google Scholar 

  3. Cazenave, T., Lions, P.L.: Orbital stability of standing waves for some nonlinear Schrödinger equations. Commun. Math. Phys.85, 549–561 (1982)

    Google Scholar 

  4. Lee, T.D.: Particle physics and introduction to field theory. New York: Harwood Academic Publishers 1981

    Google Scholar 

  5. Lions, P.L.: Principle de concentration — compacite en calcul des variations. C. R. Acad. Sci. Paris294, 261–264 (1982)

    Google Scholar 

  6. Shatah, J.M.: Unstable ground state and standing waves of nonlinear Klein-Gordon equations (to appear)

  7. Strauss, W.A.: Nonlinear invariant wave equations. In: Lecture Notes in Physics, Vol. 23, pp. 197–249 (Erice 1977). Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  8. Strauss, W.A.: Anais. Acad. Bras. Cienc.42, 645–651 (1970)

    Google Scholar 

  9. Strauss, W.A.: Existence of solitary waves in higher dimensions. Commun. Math. Phys.55, 149 (1977)

    Google Scholar 

  10. Berestycki, H., Lions, P.: Arch. Rat. Mech. Anal. (1983)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shatah, J. Stable standing waves of nonlinear Klein-Gordon equations. Commun.Math. Phys. 91, 313–327 (1983). https://doi.org/10.1007/BF01208779

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01208779

Keywords

Navigation