Generalized Structure of Lax Representations for Nonlinear Evolution Equation

Qiao Zhijun

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Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(7): 625-630

Qiao Zhijun. Generalized Structure of Lax Representations for Nonlinear Evolution Equation[J]. Applied Mathematics and Mechanics, 1997, 18(7): 625-630.

Citation:

Qiao Zhijun. Generalized Structure of Lax Representations for Nonlinear Evolution Equation[J]. Applied Mathematics and Mechanics, 1997, 18(7): 625-630.

Citation:

Qiao Zhijun. Generalized Structure of Lax Representations for Nonlinear Evolution Equation[J]. Applied Mathematics and Mechanics, 1997, 18(7): 625-630.

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Generalized Structure of Lax Representations for Nonlinear Evolution Equation

Qiao Zhijun^1,2

1.
Department of Mathematics,Liaoning University. Shenyang 110063;
2.
Institute of Mathematics, Fudan University, Shanghai 200433 P. R. China

Received Date: 1995-11-17
Rev Recd Date: 1996-10-05
Publish Date: 1997-07-15

Abstract

Abstract

A new production form for a hierarchy of nonlinear evolution equations (NLEEs)is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is thus presented. As a concrete example. the Levi-hierarchy of evolution equations are discussed at the end of this paper.
- production form,
- generalized structure,
- Levi hierarchy

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References(17)

References

[1]	Ma Wcnxiu,Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations,J.Math.Phys.,33(1992),2464-2480.
[2]	Ma Wenxiu,An approach for constructing nonisospectral hierarchies of evolution equations,T.Phys.A.Math,Gen,2(1992),719-723.
[3]	Ma Wenxiu,The algebraic structure of zero curvature representations and application to coupled KdV systems,J.Phtys.A.,Mafh.Gen 2(1993),2573-2585.
[4]	乔志军,孤子族的生成及换位表示的一般结构,应用数学学报.1(1995),287-301.
[5]	A,S,Fokas and R.L,Andersen,On the use of isospectral eigeavalue problem for obtaining hereditary symmetries for Hamiltonian systems,J.Math,Phys.,23 (1982),1066-1082.
[6]	Tu Guizhang,An extension of a theorem on gradients of conserved densities of integrable systems,Northeastern Math,J.,(1990),26-34.
[7]	Cao Cewen,Nonlinearization of the Lag equation groups for the AKNS hierarchy,Sci,China A.,33 (1990),528-536.
[8]	曹策问,保谱方程的换位表示,科学通报,3(1989),723-725.
[9]	郭福奎.Lax表示的变形与Hamilton方程族的Lax表示,数学学报,37(1994),515-525.
[10]	S,V,Manakon,L-A-B representation of integrable systems,Usp,Mat,Nauk 31 (1976),245-250.
[11]	马文秀.可积系I: A-B表示相关的代数结构.科学通报.3(1992),8-12.
[12]	乔志军,D-AKNS族的换位表示,应用数学,4(4) (1991),64-70.
[13]	乔志军,Levi族的Lag表示,科学通报,3(1990),1353-1354.
[14]	马文秀,杨族可积发展方程的换位表示.科学通报.3(1990),1843-1847.
[15]	Qiao Zhijun,Lie algebraic structure of operator related to the stationary systerns,Phbs,Lett.A.,20(1995),347-358.
[16]	D.Levi,G.Neugebauer and R.Meinal,A new nonlinear Schrodinger equation,its hierarchy and N-soliton solutions,Phys.Lett.A.,102 (1984),1-8.
[17]	Qiao Zhijun,A Barg mann system and involutive representations of solutions of the Levi hierarchy,J,Phis.A.,Math,Gen 2(1993),4407-4417.