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
This paper obtains the multi-component Harry-Dym （HI）） hierarchy and its integrable couplings by using two kinds of vector loop algebras G^-3 and G^-6. The Hamiltonian structures of the above system are given by th...This paper obtains the multi-component Harry-Dym （HI）） hierarchy and its integrable couplings by using two kinds of vector loop algebras G^-3 and G^-6. The Hamiltonian structures of the above system are given 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 production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structur...A new production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.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This paper obtains the multi-component Harry-Dym （HI）） hierarchy and its integrable couplings by using two kinds of vector loop algebras G^-3 and G^-6. The Hamiltonian structures of the above system are given 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 production form for a hierarchy of nonlinear evolution equations (NLEEs) is given in this paper. The form contains productions of isospectral and non-isospectral hierarchy. Under this form a generalized structure of Lax representations for the hierarchy of NLEEs is this presented. As a concrete example, the Levi-hierarchy of evolution equations are discussed at the end of this paper.
