In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new dis...In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.展开更多
From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equati...From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equation.One of them has complex Hamiltion structure with the help of generalized Tu formula (GTM).展开更多
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 a...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.展开更多
文摘In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.
基金Supported by the Natural Science Foundation of China under Grant Nos.60971022,61072147,and 11071159the Natural Science Foundation of Shanghai under Grant No.09ZR1410800+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101the National Key Basic Research Project of China under Grant No.KLMM0806
文摘From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebrasare obtained.Two expanding integrable systems are produced with the help of the generalized zero curvature equation.One of them has complex Hamiltion structure with the help of generalized Tu formula (GTM).
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
文摘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.
