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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
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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

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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.