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
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-b...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
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, ...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.展开更多
A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarc...A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self- consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
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 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.
基金Project supported by the Science Foundation of the Educational Department of Shandong Province of China (Grant No.J07YH01)
文摘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.
基金The National Natural Science Foundation of China(1154717511271008+1 种基金11501526)the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(2017GGJS145)
基金supported by the National Natural Science Foundation of China(Grant Nos.11547175,11271008 and 61072147)the First-class Discipline of University in Shanghai,Chinathe Science and Technology Department of Henan Province,China(Grant No.152300410230)
文摘A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self- consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy.
基金The National Natural Science Foundation of China(11547175)the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education(2017GGJS145)
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
