摘要
讨论关于表面张力的实验与理论分析之间的矛盾．把表面张力的能量当作高阶小量、导出了非传播孤立波的基本方程，得到的解与实验结果相符．
The contradictory between experiments and theory about the effect of the surface tension on the non-propagating soliton was discussed in this article. Since the lateral wave length was short, the effect of the surface tension on the non-propagating soliton was discussed by Miles and Zhou. They modified the relation between the frequency and the wave length by the surface tension, and brought it into higher order. According to the theoritical analysis, Zhou divided the kh-σ plane into three regions (Fig.1), where σ = αk2/ρg, k the wave number, h the water depth,α the surface tension coefficient, and ρ the fluid density. In the regions (1) and (2), the breathsoliton with the form sech can be produced, and the kink soliton can be formed in region (3). Butin the experiments, the breath soliton occured only if kh > 1. In the region (3), the kink soliton could not be produced and was replaced by the breath soliton when kh > 1. Miao calculated theenergy corresponding to the surface tension and the displacement of the free surface and discoveredthat the energy of the former was only 3% ～5% of that of the latter. So, the effect of the surface tension is in the higher order, and should be reconsidered theoretically.The surface tension was considered here as the same order with the forcing term. The governing equation was derived. The solution was obtained. It was shown that the breath soliton occured only if kh > 1. It is consistent with the experiments.l) The project supported by the National Natural Science foundation of China and National Basic Research 'Nonlinear Science'.
出处
《力学学报》
EI
CSCD
北大核心
1998年第6期672-675,共4页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
国家基础性研究重大项目
关键词
非传播孤立波
表面张力
孤立波
立方S方程
non-propagating soliton, surface tension, cubic Schrodinger equation, soliton
