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A seventeenth-order series expansion for the solitary wave

Published online by Cambridge University Press:  20 April 2006

Stephen A. Pennell  and
C. H. Su
Stephen A. Pennell
Affiliation:
Department of Mathematics, University of Lowell, Massachusetts 01854
C. H. Su
Affiliation:
Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912
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Abstract

The properties of solitary waves are investigated numerically using a series in sech2 ½x to describe the wave profile. (It is shown that this expansion is complete in the L2 sense.) Seventeen terms in the series are computed. For waves of amplitudes up to half the undisturbed fluid depth, the 17-term partial sum gives profiles and wave-parameter values with at least two-digit accuracy. For waves of larger amplitude, if Padé approximants are used to accelerate convergence, the computed values of the wave parameters are found to agree with the values obtained by Longuet-Higgins & Fenton (1974), but differ from those of Williams (1981), Witting (1981) and Hunter & Vanden-Broeck (1983). Possible explanations of this discrepancy are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 431 - 443
Copyright
© 1984 Cambridge University Press

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