This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which ...This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.展开更多
Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classic...Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.展开更多
Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, it...Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.展开更多
We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the a...We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.展开更多
In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the sup...In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the super-bi-Hamiltonian structure of the super-Dirac hierarchy.展开更多
基金supported by the National Key Basic Research Development of China (Grant No 2004CB318000)
文摘This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.
基金supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of the Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+1 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (S30104)
文摘Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.
基金＊Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, the Natural Science Foundation of Shanghai urlder Grant No. 09ZR1410800, the Shanghai Leading Academic Discipline Project under Grant No. J50101, and the National Key Basic Research Project of China under Grant No. KLMM0806
文摘Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11771352 and 11371293
文摘We present a variety of superintegrable systems in polar coordinates possessing a cubic and a quadratic integral of motion, where Noether integrals of kinetic energy are used to build the integrals. In addition, the associated polynomial Poisson algebras with their algebraic dependence relations are exhibited.
基金supported by the Joint Foundation of NSFC-Guangdong of China(No.U1133001/L03)
文摘In this paper, we introduce the supertrace identity and its applications. A new eight-dimensional Lie superalgebra is constructed and the super-Dirac hierarchy is derived. By the supertrace identity, we obtain the super-bi-Hamiltonian structure of the super-Dirac hierarchy.
