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Symbolic Computation of the Stokes Wave

  • W. H. Hui
  • G. Tenti

Abstract

Despite their familiarity, our understanding of the dynamics of surface water waves is far from complete, mainly because of the nonlinearity of the basic equations. G.G. Stokes was the first to find a particular solution in the form of a perturbation series. His result has been improved upon only recently, when fast electronic computers allowed researchers to carry out Stokes’ program numerically to very high order, although numerical noise precludes drawing definitive conclusions for large amplitude waves. However, the development of modern symbolic computation systems has made it possible to obtain exact results, and we report in this paper on the use of two such systems (MAPLE and MACSYMA) for this problem. Central to the success of the approach is a new mathematical formulation, particularly suitable for symbolic computation.

Keywords

Wave Height Fourier Coefficient Symbolic Computation Perturbation Series Surface Boundary Condition 
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

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Copyright information

© Kluwer Academic Publishers 1985

Authors and Affiliations

  • W. H. Hui
    • 1
  • G. Tenti
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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