A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

doi:10.1088/1674-1056/19/1/010202

中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10202-010202.doi: 10.1088/1674-1056/19/1/010202

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

王新赠, 董焕河

College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China

收稿日期:2009-03-12 修回日期:2009-04-22 出版日期:2010-01-15 发布日期:2010-01-15
基金资助:
Project supported by the Science Foundation of the Educational Department of Shandong Province of China (Grant No. J07YH01).

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

Wang Xin-Zeng(王新赠)^† and Dong Huan-He(董焕河)

College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received:2009-03-12 Revised:2009-04-22 Online:2010-01-15 Published:2010-01-15
Supported by:
Project supported by the Science Foundation of the Educational Department of Shandong Province of China (Grant No. J07YH01).

摘要/Abstract

摘要： A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.

Abstract: A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.

Key words: Lie superalgebra, supertrace identity, superintegrable system, super-Hamiltonian structure

中图分类号: (Integrable systems)

02.30.Ik

02.10.Ud (Linear algebra)

王新赠, 董焕河. A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations[J]. 中国物理B, 2010, 19(1): 10202-010202.

Wang Xin-Zeng(王新赠) and Dong Huan-He(董焕河) . A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations[J]. Chin. Phys. B, 2010, 19(1): 10202-010202.

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A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

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