A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational iden...A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.展开更多
采用介质层壳弯曲的唯象方法，在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述，其引力方程的二个条件解分别与 Newton 引力理论及 Einstein 引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性，给出了...采用介质层壳弯曲的唯象方法，在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述，其引力方程的二个条件解分别与 Newton 引力理论及 Einstein 引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性，给出了相似扩展方程，随后通过讨论天体运行轨道的基线扩展特征，给出了天体运行的离散轨道方程，并以太阳系行星及部分卫星为例，给出了这些天体运行离散轨道方程的具体表述形式．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
基金Project supported by the State Administration of Foreign Experts Affairs of Chinathe National Natural Science Foundation of China (Nos.10971136,10831003,61072147,11071159)+3 种基金the Chunhui Plan of the Ministry of Education of Chinathe Innovation Project of Zhejiang Province (No.T200905)the Natural Science Foundation of Shanghai (No.09ZR1410800)the Shanghai Leading Academic Discipline Project (No.J50101)
文摘A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations.The variational identities under non-degenerate,symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings.A special case of the suggested loop algebras yields nonlinear bi-integrable Hamiltonian couplings for the AKNS soliton hierarchy.
文摘采用介质层壳弯曲的唯象方法，在规整三维空间中给出了能量曲率方程及物体间的能量引力形式表述，其引力方程的二个条件解分别与 Newton 引力理论及 Einstein 引力理论的有关结果相近．讨论了目前分维微积分在函数方面的局限性，给出了相似扩展方程，随后通过讨论天体运行轨道的基线扩展特征，给出了天体运行的离散轨道方程，并以太阳系行星及部分卫星为例，给出了这些天体运行离散轨道方程的具体表述形式．
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.
