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1.
XIA Tie-Cheng YU Fa-Jun CHEN Deng-Yuan 《理论物理通讯》2004,42(10)
A new simple loop algebra G M is constructed, which is devoted to establishing an isospectral problem. By making use of Tu scheme, the multi-component C-KdV hierarchy is obtained. Further, an expanding loop algebra FM of the loop algebra G M is presented. Based on FM , the multi-component integrable coupling system of the multi-component C-KdV hierarchy is worked out. The method can be used to other nonlinear evolution equations hierarchy. 相似文献
2.
XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 《理论物理通讯》2005,44(6):990-996
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 相似文献
3.
XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 《理论物理通讯》2005,44(12)
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multicomponent integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 相似文献
4.
A new simple loop algebra GM is constructed, which is devoted to establishing an isospectral problem.By making use of generalized Tu scheme, the multi-component SC hierarchy is obtained. Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on FM, the multi-component integrable coupling system of the multi-component SC hierarchy of soliton equations is worked out. How to design isospectral problem of mulitcomponent hierarchy of soliton equations is a technique and interesting topic. The method can be applied to other nonlinear evolution equations hierarchy. 相似文献
5.
XIA Tie-Cheng YOU Fu-Cai 《理论物理通讯》2005,44(5):793-798
A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach. 相似文献
6.
XIA Tie-Cheng YOU Fu-Cai 《理论物理通讯》2005,44(11)
A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach. 相似文献
7.
A type of new loop algebra $\tilde{G}_M$ is constructed by making use of
the concept of cycled numbers. As its application, an isospectral problem is
designed and a new multi-component integrable hierarchy with multi-potential
functions is worked out, which can be reduced to the famous KN hierarchy. 相似文献
8.
Fukui Guo Yufeng Zhang Qingyou Yan 《International Journal of Theoretical Physics》2004,43(4):1139-1146
A new simple method for obtaining integrable hierarchies of soliton equations is proposed. First of all, a new loop algebra
is constructed, whose commutation operation is clear as that in loop algebra
. Second, by making use of the Tu scheme, many of integrable hierarchies with multicomponent potential functions can be produced. As a specific application of our method, a multicomponent AKNS hierarchy is obtained. Finally, an expanding loop algebra
of the loop algebra
is constructed. Taking advantage of
above, a type of integrable coupling system of the multicomponent AKNS hierarchy is worked out. 相似文献
9.
CHEN Lan-Xin SUN Ye-Peng ZHANG Jun-Xian 《理论物理通讯》2008,49(3):540-544
A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established. 相似文献
10.
A set of new multi-component matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A-2M. It follows that an isospectral problem is established. By making use of Tu scheme, a Liouville integrable multi-component hierarchy of soliton equations is generated, which possesses the multi-component Hamiltonian structures. As its reduction cases, the multi-component C-KdV hierarchy is given. Finally, the multi-component integrable coupling system of C-KdV hierarchy is presented through enlarging matrix spectral problem. 相似文献
11.
We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/(4). The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl(4). 相似文献
12.
The Hamiltonian structure of the integrable couplings obtained by
our method has not been solved. In this paper, the Hamiltonian
structure of the KN hierarchy is obtained by making use of the
quadratic-form identity. 相似文献
13.
In this letter, a new loop algebra G is constructed, from which a new isospectral problem is established. It follows that integrable couplings of the well-known coupled Burgers hierarchy are obtained. 相似文献
14.
XIATie-Cheng CHENXiao-Hong CHENDeng-Yuan ZHANGYu-Feng 《理论物理通讯》2004,42(2):180-182
In this letter, a new loop algebra G is constructed, from which a new isospectral problem is established. It follows that integrable couplings of the well-known coupled Burgers hierarchy are obtained. 相似文献
15.
Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy. 相似文献
16.
A new multi-component Lie algebra is constructed, and a type of new loop algebra is presented. A (2+1)-dimensional multi-component DLW integrable hierarchy is obtained by using a (2+1)-dimensional zero curvature equation. Furthermore, the loop algebra is expanded into a larger one and a type of integrable coupling system and its corresponding Hamiltonian structure are worked out. 相似文献
17.
18.
By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity. 相似文献
19.
In this paper, we extend a (2+2)-dimensional continuous zero curvature equation to (2+2)-dimensional discrete zero curvature equation, then a new (2+2)-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the (2+2)-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl(4). 相似文献
20.
DONG Huan-He SONG Ming WANG Xue-Lei LI Jian-Jun 《理论物理通讯》2008,49(5):1114-1118
A new and efficient way is presented for discrete integrable couplings with the help of two semi-direct sum Lie algebras. As its applications, two discrete integrable couplings associated with the lattice equation are worked out. The approach can be used to study other discrete integrable couplings of the discrete hierarchies of solition equations. 相似文献