数学物理学报(英文版) ›› 1983, Vol. 3 ›› Issue (4): 377-386.
谢定裕
D. Y. Hsieh
摘要: Evolution equations for the amplitudes and phases of a dominant mode of the water wave are derived by using the variational method. A. fully nonlinear dispersion relation, which is valid for finite amplitudes, is obtained when the wave is representable by a dominant sinusoidal mode. The stability criterion of the sinusoidal wave state is established and it is shown that for small amplitudes the sinusoidal wave state is stable.