A New Lie Algebra and Its Related Liouville Integrable Hierarchies

A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived...

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Bibliographic Details
Published inCommunications in theoretical physics Vol. 54; no. 9; pp. 407 - 411
Main Author 王惠 王新赠 刘国栋 杨记明
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.09.2010
Subjects
Lie代数
Liouville可积
双Hamilton结构
层次结构
循环代数
等谱问题
运营商
零曲率方程
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ISSN0253-6102
DOI10.1088/0253-6102/54/3/05

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Summary:A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
Bibliography:Lie algebra, Liouville integrable hierarchy, Hirota operator, Quadratic-form identity
O175.29
O152.5
11-2592/O3
ISSN:0253-6102
DOI:10.1088/0253-6102/54/3/05