Abstract
In this paper, the governing equation for the non-propagating solitary waves, similar to the cubic Schrödinger equation, is derived by the multiple scales with the consideration of surface tension. The non-propagating solitary wave solution is given. It is explained by the capillary-gravity wave theory that the crests are sharpened and the troughs are flattened in the transversal harmonic of the non-propagating solitary waves. On σ∼kh plane, two parameter regions are obtained in which the non-propagating solitary wave can occur, but all existing experimental parameters are in region 1 (Fig. 1).
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References
Wu J. et al.,Phys. Rev. Lett.,52 (1984), 1421–1424.
Larraza A. & Putterman S.,J. Fluid Mech.,148 (1984), 443–449.
Miles J. W.,J. Fluid Mech.,148 (1984), 451–460.
Wang B. & Wei R.,Acta Physics Sinica,35 (1986), 1547–1555.
Cui H. et al.,Acta Xiangtan Univ. (nature sciences),4 (1986), 27–34.
Yan J. & Huang G.,Acta Phys. Sinica,37 (1988), 874–880.
Yan J. & Huang G.,Applied Math. Mech.,8 (1987), 925–929.
Xu Y., Ph. D. thesis, Nanjing Univ. (1988).
Mei C. C., Applied Dynamics of Ocean Surface Waves, Wiley-Interscience (1983).
Djordjevic V. D. & Redekopp L. G.,J. Fluid Mech.,79 (1977), 703–714.
Harrison W. J.,Proc. Lond. Soc. Math.,7, 2 (1909), 107.
McGoldrick L. F.,J. Fluid Mech.,42 (1970), 193.
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Xianchu, Z., Hongnong, C. & Longwan, X. Non-propagating solitary waves with the consideration of surface tension. Acta Mech Sinica 7, 111–116 (1991). https://doi.org/10.1007/BF02486837
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DOI: https://doi.org/10.1007/BF02486837