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Applied Scientific Research

, Volume 29, Issue 1, pp 430–446 | Cite as

On the hamiltonian theory of surface waves

  • L. J. F. Broer
Article

Abstract

It is shown that the classical theory of gravity driven waves on the surface of a non-viscous liquid can be derived from a set of canonical equations. Various approximate equations then can be found by introducing suitable approximations to the kinetic and potential energy functionals. The stability of these approximate equations then can be insured beforehand by using positive definite approximate energy functionals. For fairly long, fairly low waves a stable equation of Boussinesq type is derived in this way. This equation is also valid for waves which are not approximately simple.

Keywords

Potential Energy Surface Wave Classical Theory Approximate Equation Stable Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Broer, L. J. F., Appl. Sci. Res. B11 (1964) 273.Google Scholar
  2. [2]
    Broer, L. J. F. and J. A. Kobussen, Physica 61 (1972) 275. Kobussen, J. A., Thesis, Eindhoven, 1973.Google Scholar
  3. [3]
    Broer, L. J. F. and J. A. Kobussen, Appl. Sci. Res. 29 (1974) 419.Google Scholar
  4. [4]
    Broer, L. J. F. and M. F. H. Schuurmans, J. Eng. Math. 4 (1970) 305, 5 (1971) 109.Google Scholar

Reference

  1. [1]
    Erdelyi, A., et al., Tables of integral transforms, Vol. 1., McGraw Hill, 1954.Google Scholar

Copyright information

© Martinus Nijhoff, The Hague 1974

Authors and Affiliations

  • L. J. F. Broer
    • 1
  1. 1.Dept. of PhysicsEindhoven Univ. of TechnologyEindhovenThe Netherlands

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