## 留言板

 引用本文: 周显初. 缓变的任意截面渠道中的孤立波[J]. 应用数学和力学, 1981, 2(4): 397-406.
Chou Xian-chu. The Solitary Waves in a Gradually Varying Channel of Arbitrary Cross-section[J]. Applied Mathematics and Mechanics, 1981, 2(4): 397-406.
 Citation: Chou Xian-chu. The Solitary Waves in a Gradually Varying Channel of Arbitrary Cross-section[J]. Applied Mathematics and Mechanics, 1981, 2(4): 397-406.

## The Solitary Waves in a Gradually Varying Channel of Arbitrary Cross-section

• 摘要: 本文研究了在流动方向可以有缓慢变化的任意截面渠道中的孤立波,导出了缓变系数KdV方程,并求出了此方程的首项近似解,导出了孤立波的速度的表示式,以及孤立波的波幅与渠道几何尺寸的关系,并把它们应用于三角形渠道、矩形渠道,对于变深度、变宽度矩形渠道的情况,本文的结果与Johnson、Shuto及Mile等人所得的结果一致.
•  [1] Grimshaw,R.,The solitary waves in water of variable depth.J.Fluid Mech.42,(1970) 639-656. [2] Grimshaw,R.,Long nonlinear internal waves in channels of arbitrary cross-section.J.Fluid Mech.86,(1978),415-431. [3] Johnson,R.S.,On the development of a solitary wave moving over an uneven bottom.Proc.Camb.Phil.Soc.73,(1973a),183-203. [4] Johnson,R.S.,On an asymptotic solution of the Korteweg-de Vries equation with slowly varying coefficients,J.Fluid Mech.60,(1973b),813-824. [5] Lamb,H.,Hydrodynamics,Cambridge University Press.(1932). [6] Mile,John W.,Note on a solitary wave in a slowly varying channel,J.Fluid Mech.80,(1977),149-152. [7] Mile,John W.,Solitary Waves,Annual Rev.Fluid Mech.12,(1980) 10-43. [8] Peregrine,D.H.,Long waves in a uniform channel of arbitrary cross-section,J.Fluid Mech. 32,(1968),353-365. [9] Peter,A.S.,Rotational and irrotational solitary waves in a channel with arbitrary crosssection,Comm.Pure and Appl.Math.19,No.4,(1966),445. [10] Shuto,N.,Nonlinear long waves in a channel of variable section,Coastal Engin.in Japan. 17,(1974),1-12.
##### 计量
• 文章访问数:  1670
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##### 出版历程
• 收稿日期:  1981-01-31
• 刊出日期:  1981-08-15

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