Stationary travelling waves on a film flowing down an inclined plane
Stationary travelling waves on a film flowing down an inclined plane
复制标题
沿斜面流动的薄膜上的静止行波
DOI：
10.1007/bf01089622
复制
发表时间：
1980
期刊：
影响因子：
0.9
通讯作者：
O. Tsvelodub
中科院分区：
文献类型：
--
作者：
O. Tsvelodub
在小流量下，对长波扰动的研究归结为描述膜厚变化的近似非线性方程的解[1-3]。根据线性理论[1，2]，只有当波数α接近于中性波数αn时，才能解析地得到定常波。文[4]中数值地构造了波数为0.5αn⩽α⩽αn的有限区间的周期解。在本文中，这些解几乎是在线性理论中不稳定的波数0⩽α⩽αn的完整范围内找到的。特别地，得到了该方程的孤子解。研究结果部分发表在文献[5]上。
At small flow rates, the study of long-wavelength perturbations reduces to the solution of an approximate nonlinear equation that describes the change in the film thickness [1–3]. Steady waves can be obtained analytically only for values of the wave numbers α close to the wave number αn that is neutral in accordance with the linear theory [1, 2]. Periodic solutions were constructed numerically for the finite interval of wave numbers 0.5αn ⩽ α ⩽ αn in [4]. In the present paper, these solutions are found in almost the complete range of wave numbers 0 ⩽ α ⩽ αn that are unstable in the linear theory. In particular, soliton solutions of this equation are obtained. The results were partly published in [5].