| A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system |
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| 作者姓名： | 杨红丽 宋金宝 杨联贵 刘永军 |
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| 作者单位： | Institute of Oceanology, Chinese Academy of
Sciences, Qingdao 266071,
China;Graduate School, Chinese Academy of Sciences, Beijing
100049, China;Institute of Oceanology, Chinese Academy of
Sciences, Qingdao 266071,
China;Department of Mathematics, Inner Mongolia University,
Hohhot 010021, China;Institute of Oceanology, Chinese Academy of
Sciences, Qingdao 266071,
China;Graduate School, Chinese Academy of Sciences, Beijing
100049, China |
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| 基金项目： | Project
supported by the National Science Fund for Distinguished Young
Scholars (Grant No 40425015). |
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| 摘 要： | This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters： the nonlinearity ratio ε, represented by the ratio of amplitude to depth, and the dispersion ratio μ, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O（μ^2）. As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.
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| 关 键 词： | 流动性系统 人工波 方程组 计算方法 |
| 文章编号： | 1009-1963/2007/16（12）/3589-06 |
| 收稿时间： | 2007-01-03 |
| 修稿时间： | 2007-03-28 |
A kind of extended Korteweg--de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system |
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| Yang Hong-Li,Song Jin-Bao,Yang Lian-Gui and Liu Yong-Jun.A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system[J].Chinese Physics B,2007,16(12):3589-3594. |
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| Authors: | Yang Hong-Li Song Jin-Bao Yang Lian-Gui and Liu Yong-Jun |
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| Affiliation: | Department of Mathematics, Inner Mongolia University,
Hohhot 010021, China; Institute of Oceanology, Chinese Academy of
Sciences, Qingdao 266071,
China; Institute of Oceanology, Chinese Academy of
Sciences, Qingdao 266071,
China;Graduate School, Chinese Academy of Sciences, Beijing
100049, China |
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| Abstract: | This paper considers interfacial waves propagating along the
interface between a two-dimensional two-fluid with a flat bottom and
a rigid upper boundary. There is a light fluid layer overlying a
heavier one in the system, and a small density difference exists
between the two layers. It just focuses on the weakly non-linear
small amplitude waves by introducing two small independent
parameters: the nonlinearity ratio $\varepsilon $, represented by
the ratio of amplitude to depth, and the dispersion ratio $\mu $,
represented by the square of the ratio of depth to wave length,
which quantify the relative importance of nonlinearity and
dispersion. It derives an extended KdV equation of the interfacial
waves using the method adopted by Dullin {\it et al} in the study of
the surface waves when considering the order up to $O(\mu ^2)$. As
expected, the equation derived from the present work includes, as
special cases, those obtained by Dullin {\it et al} for surface
waves when the surface tension is neglected. The equation derived
using an alternative method here is the same as the equation
presented by Choi and Camassa. Also it solves the equation by
borrowing the method presented by Marchant used for surface waves,
and obtains its asymptotic solitary wave solutions when the weakly
nonlinear and weakly dispersive terms are balanced in the extended
KdV equation. |
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| Keywords: | two-fluid system interfacial
waves extended KdV equation solitary wave solution |
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