Stability of some stationary solutions to the forced KdV equation with one or two bumps
Stability of some stationary solutions to the forced KdV equation with one or two bumps
复制标题
具有一两个凸点的受迫 KdV 方程的一些平稳解的稳定性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Vanden
中科院分区：
文献类型：
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作者：
Frédéric Chardard;F. Dias;Hai Yen Nguyen;J. Vanden
本文研究了自由面绕流淹没障碍物的问题。假设流体是无粘且不可压缩的，并且流动是无旋的。对一个或两个凸块上的长非线性表面波进行一阶近似，得到一个受迫的Korteweg-de弗里斯（fKdV）方程。固定fKdV方程的解决方案的构造和他们的稳定性进行了研究，无论是解析或数值。这些不同的解决方案，包括孤立波在一个单一的凸块，孤立波与两个驼峰在一个双凸块，桌面解决方案在一个双凸块和前。
Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The first-order approximation of long nonlinear surface waves over one or two bumps results in a forced Korteweg–de Vries (fKdV) equation. Solutions of the stationary fKdV equation are constructed and their stability is studied, either analytically or numerically. These various solutions include solitary waves over a single bump, solitary waves with two humps over a double bump, table-top solutions over a double bump and fronts.