Acta Mathematica

On the stokes conjecture for the wave of extreme form

C. J. Amick, L. E. Fraenkel, and J. F. Toland

Full-text: Open access

Article information

Source
Acta Math., Volume 148 (1982), 193-214.

Dates
Received: 6 July 1981
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485890159

Digital Object Identifier
doi:10.1007/BF02392728

Mathematical Reviews number (MathSciNet)
MR666110

Zentralblatt MATH identifier
0495.76021

Rights
1982 © Almqvist & Wiksell

Citation

Amick, C. J.; Fraenkel, L. E.; Toland, J. F. On the stokes conjecture for the wave of extreme form. Acta Math. 148 (1982), 193--214. doi:10.1007/BF02392728. https://projecteuclid.org/euclid.acta/1485890159


Export citation

References

  • Amick, C. J. & Fraenkel, L. E., On the behaviour near the creast of waves of extreme form. To appear.
  • Amick, C. J. & Toland, J. F., On solitary water-waves of finite amplitude. Arch. Rational Math. Anal., 76 (1981), 9–95.
  • — 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.
  • Cokelet, E. D., Steep gravity waves in water of arbitrary uniform depth. Philos. Trans. Roy. Soc. London, A 286 (1977), 183–230.
  • Keady, G. & Norbury, J., On the existence theory for irrotational water waves. Math. Proc. Cambridge Philos. Soc., 83 (1978), 137–157.
  • 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.
  • Longuet-Higgins, M. S. & Fox, M. J. H., Theory of the almost highest wave: the inner solution. J. Fluid Mech., 80 (1977), 721–742.
  • 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 in Math. Proc. Cambridge Philos. Soc.
  • 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.
  • —, 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.
  • 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.