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The phenomenon of three-dimensional capillary gravity waves on deep water is considered. The solution is obtained by bifurcation from a two-dimensional wave into three-dimensional waves composed of the two-dimensional wave plus a pair of oblique waves. The streamwise period of the three-dimensional waves is doubled, and there is another period in the spanwise direction. The speed and the stability of the three-dimensional waves are discussed.
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Yan‐Chow Ma (1982) studied this question.
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