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Whitham-Broer-Kaup浅水波方程的Backlund变换和精确解

 引用本文: 范恩贵, 张鸿庆. Whitham-Broer-Kaup浅水波方程的Backlund变换和精确解[J]. 应用数学和力学, 1998, 19(8): 667-670.
Fan Engui, Zhang Hongqing. Backlund Transformation and Exact Solutions for Whitham-Broer-Kaup Equations in Shallow Water[J]. Applied Mathematics and Mechanics, 1998, 19(8): 667-670.
 Citation: Fan Engui, Zhang Hongqing. Backlund Transformation and Exact Solutions for Whitham-Broer-Kaup Equations in Shallow Water[J]. Applied Mathematics and Mechanics, 1998, 19(8): 667-670.

• 中图分类号: O175

## Backlund Transformation and Exact Solutions for Whitham-Broer-Kaup Equations in Shallow Water

• 摘要: 用一种新的方法并借助Mathematica,求出了Whitham-Broer-Kaup(简记WBK)方程的一种Backlund变换,并建立了WBK方程与热传导方程及Burgers方程的联系.利用这种关系得到了WBK方程的三组精确解,其中一组为孤波解.
•  [1] G.B.Whitham,Variational methods and applications to water wave,Proc.Roy.Soc.London,Ser.A,299(1456)(1967),6-25. [2] L.J.Broer,Approximate equations for long water waves,Appl.Sci.Res.,31(5)(1975),377-395. [3] D.J.Kaup,A higher-order water wave equation and method for solvingit,Prog.Theor.Phys.,54(2)(1975),396-408. [4] B.A.Kapershmidt,Mathematics of dispersive water waves,Comm.Math.Phys.,99(1)(1985),51-73. [5] M.J.Ablowitz,Soliton,Nonlinear Evolution Equations and Inverse Scatting,Cambridge University Press(1991). [6] H.Q.Zhang and F.X.Wu,Mechanical method to construct the general solution for system of partia differential equations,Proc.1992 Inter.Wor kshop Math.Mech.,Beijing,International Academi(1992),280-285. [7] 郭柏灵,《孤立子》,科学出版社(1987).

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##### 出版历程
• 收稿日期:  1997-01-03
• 修回日期:  1998-02-27
• 刊出日期:  1998-08-15

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