Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational ide...Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.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 propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4× 4 block mat...We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4× 4 block matrix Lie algebras. We apply the approach to the AKNS soIRon hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity.展开更多
基金Supported by the Fundamental Research Funds of the Central University under Grant No. 2010LKS808the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL021
文摘Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.
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 in part by the Department of Mathematics and Statistics of University of South Floridathe State Administration of Foreign Experts Affairs of China+2 种基金the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Shanghai Leading Academic Discipline Project No.J50101the National Natural Science Foundation of China under Grant Nos.11271008,61072147,and11071159
文摘We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4× 4 block matrix Lie algebras. We apply the approach to the AKNS soIRon hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity.
