A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

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	A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system
	Yang Hong-Li 1,3; Song Jin-Bao 1; Yang Lian-Gui 2; Liu Yong-Jun 1,3
刊名	CHINESE PHYSICS
	2007-12-01
卷号	16 期号:12 页码:3589-3594
关键词	Two-fluid System Interfacial Waves Extended Kdv Equation Solitary Wave Solution
ISSN号	1009-1963
文献子类	Article
英文摘要	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 epsilon, 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 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 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.; 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 epsilon, 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 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 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.
语种	英语
WOS记录号	WOS:000251993200006
公开日期	2010-12-30
内容类型	期刊论文
源URL	[http://ir.qdio.ac.cn/handle/337002/6249]
专题	海洋研究所_海洋环流与波动重点实验室
作者单位	1.Chinese Acad Sci, Inst Oceanol, Qingdao 266071, Peoples R China 2.Inner Mongolia Univ, Dept Math, Hohhot 010021, Peoples R China 3.Chinese Acad Sci, Grad Sch, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Yang Hong-Li,Song Jin-Bao,Yang Lian-Gui,et al. A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system[J]. CHINESE PHYSICS,2007,16(12):3589-3594.
APA	Yang Hong-Li,Song Jin-Bao,Yang Lian-Gui,&Liu Yong-Jun.(2007).A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system.CHINESE PHYSICS,16(12),3589-3594.
MLA	Yang Hong-Li,et al."A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system".CHINESE PHYSICS 16.12(2007):3589-3594.