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

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

Institute of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China

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.
- WBK方程 /
- Backlund变换 /
- 精确解 /
- 孤波解
Abstract: By using a new method and Mathematica,the Backlund transformations for Whitham-Broer-Kaup equations(WBK)are derived.The connections between WBK equation,heat equation and Burgers equation are found,which are used to obtain three families of solutions for WBK equations, one of which is the family of solitary wave solutions.
- WBK equation /
- Backlund transformation /
- exact solution /
- solitary wave solution

[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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