The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and （2＋l）-dimensional Guo hierarchy are obtained ...The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and （2＋l）-dimensional Guo hierarchy are obtained by the quadraticform identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.展开更多
A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this p...A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.展开更多
Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltoni...Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained.展开更多
Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplin...Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.展开更多
With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quad...With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quadratic-form identity.展开更多
A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obt...A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.展开更多
A general Lie algebra Vs and the corresponding loop algebra Vx are constructed, from which the linear isospectral Lax pairs are established, whose compatibility presents the zero curvature equation. As its application...A general Lie algebra Vs and the corresponding loop algebra Vx are constructed, from which the linear isospectral Lax pairs are established, whose compatibility presents the zero curvature equation. As its application, a new Lax integrable hierarchy containing two parameters is worked out. It is not Liouville-integrable, however, its two reduced systems are Liouville-integrable, whose Hamiltonian structures are derived by making use of the quadratic-form identity and the γ formula （i.e. the computational formula on the constant γ appeared in the trace identity and the quadratic-form identity）.展开更多
In this paper,we obtain integrable couplings of the TB hierarchy using the new subalgebra of the loop algebra A.Then the Hamiltonian structure of the above system is given by the quadratic-form identity.
In this paper,an extended loop algebra is constructed from which an isospectral problem established.It follows that the integrable couplings of the Tu hierarchy and M-AKNS-KN hierarchy are obtained,and their Hamilton ...In this paper,an extended loop algebra is constructed from which an isospectral problem established.It follows that the integrable couplings of the Tu hierarchy and M-AKNS-KN hierarchy are obtained,and their Hamilton structures are presented by the quadratic-form identity.Moreover,we guarantee that the expanding model we obtained are also Liouville integrable.展开更多
文摘The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the multi-component Guo hierarchy, integrable coupling of Guo hierarchy and （2＋l）-dimensional Guo hierarchy are obtained by the quadraticform identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies.
文摘A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.
基金in part supported by the Natural Science Foundation of China(GrantNo.11271008)the First-class Discipline of University in Shanghai and the Shanghai Univ.Leading Academic Discipline Project(A.13-0101-12-004)
文摘Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained.
文摘Firstly, a vector loop algebra G3 is constructed, by use of it multi-component KN hierarchy is obtained. Further, by taking advantage of the extending vector loop algebras G6 and G9 of G3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively. Finally, Hamiltonian structures of obtained system are given by quadratic-form identity.
文摘With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quadratic-form identity.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806
文摘A new Lie algebra G and its two types of loop algebras G1 and G2 are constructed. Basing on G1 and G2, two different isospectral problems are designed, furthermore, two Liouville integrable soliton hierarchies are obtained respectively under the framework of zero curvature equation, which is derived from the compatibility of the isospectral problems expressed by Hirota operators. At the same time, we obtain the Hamiltonian structure of the first hierarchy and the bi-Hamiltonian structure of the second one with the help of the quadratic-form identity.
基金The project supported by National Natural Science Foundation of China under Grant No. 10471139
文摘A general Lie algebra Vs and the corresponding loop algebra Vx are constructed, from which the linear isospectral Lax pairs are established, whose compatibility presents the zero curvature equation. As its application, a new Lax integrable hierarchy containing two parameters is worked out. It is not Liouville-integrable, however, its two reduced systems are Liouville-integrable, whose Hamiltonian structures are derived by making use of the quadratic-form identity and the γ formula （i.e. the computational formula on the constant γ appeared in the trace identity and the quadratic-form identity）.
文摘In this paper,we obtain integrable couplings of the TB hierarchy using the new subalgebra of the loop algebra A.Then the Hamiltonian structure of the above system is given by the quadratic-form identity.
文摘In this paper,an extended loop algebra is constructed from which an isospectral problem established.It follows that the integrable couplings of the Tu hierarchy and M-AKNS-KN hierarchy are obtained,and their Hamilton structures are presented by the quadratic-form identity.Moreover,we guarantee that the expanding model we obtained are also Liouville integrable.
