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A note on the exact solutions for non-conservative three-wave resonance

Published online by Cambridge University Press:  14 November 2011

A. D. D. Craik
A. D. D. Craik
Affiliation:
Department of Applied Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, U.K.
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Synopsis

Exact solutions recently discovered for non-conservative three-wave resonance are here related to the ‘one-lump’ solutions obtained by Backlund transformation in conservative cases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 205 - 207
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

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3Craik, A. D. D.. Exact solutions of non-conservative equations for three-wave and secondharmonic resonance. Proc. Roy. Soc. Lond. Ser. A 406 (1986), 1–12.Google Scholar
4Kaup, D. J.. The lump solutions of the Backlund transformation for the three-dimensional three-wave resonant interaction. J. Math. Phys. 22 (1981), 1176–81.CrossRefGoogle Scholar
5Zakharov, V. E.. Exact solutions to the problem of the parametric interaction of three-dimensional wave-packets. Dokl. Akad. Nauk SSSR 228 (1976) 1314–6; Soviet Phys. Dokl. 21, 322–3.Google Scholar