Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-30T08:42:16.739Z Has data issue: false hasContentIssue false
  • English
  • Français

On the change of amplitude of interacting solitary waves

Published online by Cambridge University Press:  21 April 2006

J. G. B. Byatt-Smith
J. G. B. Byatt-Smith
Affiliation:
Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the solitary-wave solutions of the Euler equations of motion are treated as a perturbation of the KdV equaton. We show analytically, that the amplitudes to two solitary waves are altered after interaction. This change in amplitude is calculated, showing that the smaller wave dereases in amplitude and the larger wave increases in amplitude.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 182 , September 1987 , pp. 485 - 497
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Boussinesq, M. J. 1872 J. Math. Pures Appl. (2), 17, 55.
Byatt-Smith, J. G. B. 1987 J. Fluid Mech. 182, 467.
Ertekin, R. C. 1984 Soliton generation by moving disturbances in shallow water: theory, computation and experiment. Ph.D. thesis, University of California, Berkeley.
Ertekin, R. C., Webster, W. C. & Wehausen, J. V. 1984 Proc. 15th Symp. Naval Hydrodynamics, Hamburg, pp. 347–361. Washington D.C: National Academy Press.
Ertekin, R. E., Webster, W. C. & Wehausen, J. V. 1986 J. Fluid Mech. 169, 275.
Fenton, J. D. & Rienecker, M. M. 1982 J. Fluid Mech. 118, 411.
Huang, De-B., Sibul, O. J., Webster, W. C., Wehausen, J. V., Wu, de-M. & Wu, T. Y. 1982 Ships moving in the transcritical range. In Proc. Conf. on Behavior of Ships in Restricted Waters, vol. 2. Varna.
Johnson, R. S. 1982 J. Fluid Mech. 120, 49.
Karpman, V. I. & Maslov, E. M. 1977a Phys. Lett. 60A, 307.
Karpman, V. I. & Maslov, E. M. 1977b Phys. Lett. 61A, 355.
Karpman, V. I. & Maslov, E. M. 1977c Sov. Phys., J. Exp. Theor. Phys. 73, 537.
Kaup, D. J. & Newell, A. C. 1978 Proc. R. Soc. Lond. A 361, 413.
Keener, J. & McLaughlin, D. W. 1977 Phys. Rev. A16, 777.
Korteweg, D. J. & de Vries, G. 1895 Phil. Mag. 39, 422.
Laitone, E. V. 1960 J. Fluid Mech. 9, 430.
Longuet-Higgins, M. S. & Fenton, J. D. 1974 On the mass momentum, energy and circulation of a solitary wave II. Proc. R. Soc. Lond. A 340, 471.Google Scholar
Mckean, H. P. & van Morbeke, P. 1975 Invent. Math. 30, 217.
Miles, J. W. 1977 J. Fluid Mech. 79, 157.
Scott-Russell, R. 1844 In Rep. of the 14th Meeting of the British Association for the Advancement of Science, York, pp. 311–390. London: John Murray.
Su, C. H. & Mirie, R. M. 1980 J. Fluid Mech. 98, 509.
Su, C. H. & Mirie, R. M. 1982 J. Fluid Mech. 115, 475.