Capillary-gravity interfacial waves in infinite depth
Capillary-gravity interfacial waves in infinite depth
复制标题
无限深度的毛细管重力界面波
DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
G. Iooss
中科院分区：
文献类型：
--
作者：
F. Dias;G. Iooss
我们考虑孤立波在两个无限层的完美流体之间的界面上的传播，当线性相速度和群速度相等时，孤立波从一列无穷小周期波分叉。该问题被简化为一个常微分方程组，并将其转化为规范形式。这种简化方法不同于有限深度的情况。规范形的分析强烈依赖于主导三次非线性系数的符号。这个符号由sgn（R-Rc）给出，其中R表示密度比，Rc是R的临界值，等于（21-8 5）/11 0.283。若R-Rc 0，则得到孤立波分支，同宿于同一周期波，在+∞和-∞处有相移.我们考虑的过渡区，其中R R c，即参数制度，其中五阶非线性的影响是可比的立方非线性。
We consider the propagation of solitary waves at the interface between two infinite layers of perfect fluids, which bifurcate from a train of infinitesimal periodic waves when the linear phase and group velocities are equal. The problem is reduced to a system of ordinary differential equations, which is put in normal form. The reduction method differs from the case of finite depth. The analysis of the normal form depends strongly on the sign of the coefficient of the leading cubic nonlinearity. This sign is given by sgn (R - R c ), where R denotes the ratio of densities and R c a critical value of R equal to (21-8√5)/11 0.283. If R - R c 0, one obtains a bifurcation of solitary waves, homoclinic to the same periodic wave with a phase shift at +∞ and -∞. We consider the transition region where R R c , i.e. the parameter regime in which the effects of quintic nonlinearity are comparable with those of cubic nonlinearity.