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Weakly non-linear, slowly varying waves and their instabilities

Published online by Cambridge University Press:  24 October 2008

R. Grimshaw
R. Grimshaw
Affiliation:
University of Melbourne
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Abstract

A non-linear Klein–Gordon equation is used to discuss the theory of slowly varying, weakly non-linear wave trains. An averaged variational principle is used to obtain transport equations for the slow variations which incorporate the leading order modulation and non-linear terms. Linearized transport equations are used to discuss instabilities.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 95 - 104
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Brooke, Benjamin T. and Feir, J. E. J.Fluid Mech. 27 (1967), 417.Google Scholar
(2)Benney, D. J. and Roskes, G. J.Studies in Applied Mathematics 48 (1969), 377.CrossRefGoogle Scholar
(3)Bisshopp, F. J.Differential Equations, 5 (1969) 592.CrossRefGoogle Scholar
(4)Bisshopp, F.Technical Report No. 9. (Division of Applied Mathematics, Brown University 1969).Google Scholar
(5)Chu, V. H. and Mei, C. C. J.Fluid Mech. 41 (1970), 873.CrossRefGoogle Scholar
(6)Luke, J. C.Proc. Roy. Soc. Ser. A 292 (1966), 403.Google Scholar
(7)Whitham, G. B.Proc. Roy. Soc. Ser. A 283 (1965), 238.Google Scholar
(8)Whitham, G. B. J.Fluid Mech. 44 (1970), 373.CrossRefGoogle Scholar
(9)Young-Ping, Pao and Su, C. H. J.Math. Mech. 19 (1970), 951.Google Scholar