摘要
A new Lie algebra G and its two types of loop algebras (?)_1 and (?)2 are constructed.Basing on (?)_1 and(?)_2,two different isospectral problems are designed,furthermore,two Liouville integrable soiiton hierarchies are obtainedrespectively under the framework of zero curvature equation,which is derived from the compatibility of the isospectralproblems expressed by Hirota operators.At the same time,we obtain the Hamiltonian structure of the first hierarchyand the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
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.
基金
Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800
the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
