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An examination of Whitham's exact averaged variational principle

Published online by Cambridge University Press:  24 October 2008

A. D. Gilbert
Affiliation:
Fluid Mechanics Research Institute, University of Essex

Extract

Whitham's exact averaged variational principle is found by a new method. Comparisons are drawn between this method and the method advanced by Whitham. Further results about the Euler equations from this variational principle are obtained.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Bretherton, F. P.Propagation in slowly varying waveguides. Proc. Roy. Soc. (London), Ser. A 302 (1969), 555.Google Scholar
(2)Bretherton, F. P. and Garrett, C. J. R.Wavetrains in inhomogeneous moving media. Proc. Roy. Soc. (London), Ser. A 302 (1969), 529.Google Scholar
(3)Cole, J. D.Perturbation methods in applied mathematics (Blaisdell, 1968).Google Scholar
(4)Dougherty, J. P.Lagrangian methods in plasma dynamics. I. General theory of the method of the averaged Lagrangian. J. Plasma Physics 4 (1970), 761.CrossRefGoogle Scholar
(5)Luke, J. C.A perturbation method for nonlinear dispersive wave problems. Proc. Roy. Soc. (London), Ser. A 292 (1966), 403.Google Scholar
(6)Minorsky, N.Nonlinear oscillations (Van Nostrand, 1962).Google Scholar
(7)Reiss, E. L.On multivariable asymptotic expansions. SIAM Review 13 (1971), 189.CrossRefGoogle Scholar
(8)Whitham, G. B.Non-linear dispersive waves. Proc. Roy. Soc. (London), Ser. A 283 (1965), 238.Google Scholar
(9)Whitham, G. B.A general approach to linear and non-linear dispersive waves using a Lagrangian. J. Fluid Mech. 22 (1965), 273.CrossRefGoogle Scholar
(10)Whitham, G. B.Non-linear dispersion of water waves. J. Fluid Mech. 27 (1967), 399.CrossRefGoogle Scholar
(11)Whitham, G. B.Variational methods and applications to water waves. Proc. Roy. Soc. (London), Ser. A 299 (1967), 6.Google Scholar
(12)Whitham, G. B.Two-timing, variational principles and waves. J. Fluid Mech. 44 (1970), 373.CrossRefGoogle Scholar