Skip to main content
Log in

On the stokes conjecture for the wave of extreme form

  • Published:
Acta Mathematica

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.

References

  1. Amick, C. J. & Fraenkel, L. E., On the behaviour near the creast of waves of extreme form. To appear.

  2. Amick, C. J. &Toland, J. F., On solitary water-waves of finite amplitude.Arch. Rational Math. Anal., 76 (1981), 9–95.

    MATH  MathSciNet  Google Scholar 

  3. — On periodic water-waves and their convergence to solitary waves in the long-wave limit.Math. Research Center report no. 2127 (1981),University of Wisconsin, Madison. Also,Philos. Trans. Roy. Soc. London, A 303 (1981), 633–669.

    MathSciNet  Google Scholar 

  4. Cokelet, E. D., Steep gravity waves in water of arbitrary uniform depth.Philos. Trans. Roy. Soc. London, A 286 (1977), 183–230.

    MATH  MathSciNet  Google Scholar 

  5. Keady, G. &Norbury, J., On the existence theory for irrotational water waves.Math. Proc. Cambridge Philos. Soc., 83 (1978), 137–157.

    Article  MATH  MathSciNet  Google Scholar 

  6. Krasovskii, Yu. P., On the theory of steady-state waves of large amplitude.U.S.S.R. Computational Math. and Math. Phys., 1 (1961), 996–1018.

    Article  MATH  MathSciNet  Google Scholar 

  7. Longuet-Higgins, M. S. &Fox, M. J. H., Theory of the almost highest wave: the inner solution.J. Fluid Mech., 80 (1977), 721–742.

    Article  MATH  MathSciNet  Google Scholar 

  8. McLeod, J. B., The Stokes and Krasovskii conjectures for the wave of greatest height.Math. Research Center report no. 2041 (1979),University of Wisconsin, Madison. Also to appear inMath. Proc. Cambridge Philos. Soc.

  9. Stokes, G. G., On the theory of oscillatory waves.Trans. Cambridge Philos. Soc. 8 (1847), 441–455. Also,Mathematical and physical papers, vol. I. pp. 197–219, Cambridge, 1880.

    Google Scholar 

  10. —, Considerations relative to the greatest height of oscillatory irrotational waves which can be propagated without change of form.Mathematical and physical papers., vol. I, pp. 225–228, Cambridge, 1880.

    Google Scholar 

  11. Toland, J. F., On the existence of a wave of greatest height and Stokes's conjecture.Proc. Roy. Soc. London, A 363 (1978), 469–485.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amick, C.J., Fraenkel, L.E. & Toland, J.F. On the stokes conjecture for the wave of extreme form. Acta Math 148, 193–214 (1982). https://doi.org/10.1007/BF02392728

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392728

Keywords

Navigation