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
A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl（4） is presented by Yu. Based on this method, we construct a new integrable couplings of the classical-Bou...A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl（4） is presented by Yu. Based on this method, we construct a new integrable couplings of the classical-Boussinesq hierarchy with self-consistent sources by using of loop algebra sl（4）. In this paper, we also point out that there exist some errors in Yu＇s paper and have corrected these errors and set up new formula. The method can be generalized other soliton hierarchy with self-consistent sources.展开更多
We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-c...We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.展开更多
Based on the generalization of Lie algebra An- 1, two types of new Lie algebras were worked out and the integrability of the related hierarchies of evolution equations were proved in the sense of Liouville.
Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvatureequation by using two higher dimension Lie algebras.Furthermore,a complex Hamiltonian structures of the secondintegr...Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvatureequation by using two higher dimension Lie algebras.Furthermore,a complex Hamiltonian structures of the secondintegrable couplings is presented by taking use of the variational identity.展开更多
基金Supported by the National Nature Science Foundation of China(11401392)the Scientific Research Fund of Liaoning Provincial Education Department(L2015378)
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.
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+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101by Key Disciplines of Shanghai Municipality (S30104)
文摘A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with sl（4） is presented by Yu. Based on this method, we construct a new integrable couplings of the classical-Boussinesq hierarchy with self-consistent sources by using of loop algebra sl（4）. In this paper, we also point out that there exist some errors in Yu＇s paper and have corrected these errors and set up new formula. The method can be generalized other soliton hierarchy with self-consistent sources.
基金Supported by the Research Work of Liaoning Provincial Development of Education under Grant No.L2010513
文摘We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.J50101)the Science Foundation of Shanghai Municiple Commission of Education (Grant No.06AZ081)
文摘Based on the generalization of Lie algebra An- 1, two types of new Lie algebras were worked out and the integrability of the related hierarchies of evolution equations were proved in the sense of Liouville.
文摘Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvatureequation by using two higher dimension Lie algebras.Furthermore,a complex Hamiltonian structures of the secondintegrable couplings is presented by taking use of the variational identity.
