A seventeenth-order series expansion for the solitary wave
- 1 December 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 149 (-1) , 431-443
- https://doi.org/10.1017/s0022112084002731
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.Keywords
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