A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of t...A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.展开更多
We propose a class of non-semisimple matrix loop algebras consisting of 3×3 block matrices,and form zero curvature equations from the presented loop algebras to generate bi-integrable couplings.Applications are m...We propose a class of non-semisimple matrix loop algebras consisting of 3×3 block matrices,and form zero curvature equations from the presented loop algebras to generate bi-integrable couplings.Applications are made for the AKNS soliton hierarchy and Hamiltonian structures of the resulting integrable couplings are constructed by using the associated variational identities.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
A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A 2M . Then we use the idea of enlarging spectral problems to make an enlarged spectral problems. It follows that the mu...A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A 2M . Then we use the idea of enlarging spectral problems to make an enlarged spectral problems. It follows that the multi-component AKNS hierarchy is presented. Further, two classes of integrable coupling of the AKNS hierarchy are obtained by enlarging spectral problems.展开更多
基金supported by Science Foundation of the Educational Department of Shandong Province of China
文摘A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.
基金This work was supported by the Department of Mathematics and Statistics of the University of South Florida,the State Administration of Foreign Experts Affairs of China,the Natural Science Foundation of Shanghai(No.09ZR1410800)the National Natural Science Foundation of China(Nos.10971136,10831003,61072147 and 11071159)Chunhui Plan of the Ministry of Education of China.J.H.Meng and W.X.Ma/Adv.Appl.Math.Mech.,5(2013),pp.652-670669 References。
文摘We propose a class of non-semisimple matrix loop algebras consisting of 3×3 block matrices,and form zero curvature equations from the presented loop algebras to generate bi-integrable couplings.Applications are made for the AKNS soliton hierarchy and Hamiltonian structures of the resulting integrable couplings are constructed by using the associated variational identities.
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.
文摘A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A 2M . Then we use the idea of enlarging spectral problems to make an enlarged spectral problems. It follows that the multi-component AKNS hierarchy is presented. Further, two classes of integrable coupling of the AKNS hierarchy are obtained by enlarging spectral problems.
