Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T07:43:12.606Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpretation of three-soliton interactions in terms of resonant triads

Published online by Cambridge University Press:  12 April 2006

D. Anker  and
N. C. Freeman
D. Anker
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
N. C. Freeman
Affiliation:
School of Mathematics, University of Newcastle upon Tyne, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The three-soliton solution of the two-dimensional Korteweg-de Vries equation is analysed to show that the structure of the interaction can be represented in terms of the motion of two-soliton resonant interactions (resonant triads) as described by Miles (1977). The schematic development of the interaction with time is obtained and shown to approximate closely to computer calculations of the analytic solution. Similar results follow for interactions of more solitons and other equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 1 , 12 July 1978 , pp. 17 - 31
Copyright
© 1978 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.)

References

Anker, D. & Freeman, N. C. 1978 Proc. Roy. Soc. A 360, 1703.
Davey, A. & Freeman, N. C. 1975 Proc. Roy. Soc. A 344, 427–433.
Davey, A. & Stewartson, K. 1974 Proc. Roy. Soc. A 338, 101–110.
Kadomtsev, B. B. & Petviashvili, V. I. 1970 Dokl. Akad. Nauk SSR 192, 753–756.
Miles, J. W. 1977 J. Fluid Mech. 79, 171–179.
Satsuma, J. 1976 J. Phys. Soc. Japan 40, 286–290.
Zakharov, V. E. & Shabat, A. B. 1974 Functional Anal. Appl. 8, 226–235.