共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
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.
Multi-component Dirac equation hierarchy and its multi-component integrable couplings system 总被引:2,自引:0,他引:2 下载免费PDF全文
A general scheme for generating a multi-component
integrable equation hierarchy is proposed. A simple
3M-dimensional loop algebra \tilde{X} is produced. By taking
advantage of \tilde{X}, a new isospectral problem is established
and then by making use of the Tu scheme the multi-component Dirac
equation hierarchy is obtained. Finally, an expanding loop algebra
\tilde{F}M of the loop algebra \tilde{X} is presented. Based
on the \tilde{F}M, the multi-component integrable coupling
system of the multi-component Dirac equation hierarchy is
investigated. The method in this paper can be applied to other
nonlinear evolution equation hierarchies. 相似文献
6.
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
7.
XIATie-Cheng YUFa-Jun CHENDeng-Yuan 《理论物理通讯》2004,42(4):494-496
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 F^-M of the loop algebra G^-M is presented. Based on F^-M , 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
8.
A new isospectral problem is established by constructing a simple interesting loop algebra. A commutation operation of the loop algebra is as straightforward as the loop algebra ?_1. It follows that a type of multi-component integrable hierarchy is obtained. This can be used as a general method. 相似文献
9.
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
10.
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
11.
DONG Huan-He ZHANG Ning 《理论物理通讯》2005,44(12)
A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra AM-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy. 相似文献
12.
A Multi-component Matrix Loop Algebra and Its Application 总被引:3,自引:0,他引:3
DONG Huan-He ZHANG Ning 《理论物理通讯》2005,44(6):997-1001
A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra A^- M-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy. 相似文献
13.
A new simple loop algebra is constructed, which is devote to establishing an isospectral problem. By making use of Tu scheme,
NLS-MKdV hierarchy is obtained. Again via expanding the loop algebra above, another higher-dimensional loop algebra is presented.
It follows that an integrable coupling of NLS-MkdV hierarchy is given. Also, the trace identity is extended to the quadratic-form
identity and the Hamiltonian structures of the NLS-MKdV hierarchy and integrable coupling of NLS-MkdV hierarchy are obtained
by the quadratic-form identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings
or multi-component hierarchies. 相似文献
14.
A set of new matrix Lie algebra and its corresponding loop algebra are constructed. By making use of Tu scheme, a Liouville
integrable multi-component hierarchy of soliton equation is generated. As its reduction cases, the multi-component Tu hierarchy
is given. Finally, the multi-component integrable coupling system of Tu hierarchy is presented through enlarging matrix spectral
problem. 相似文献
15.
The multi-component Tu hierarchy of soliton equations and its multi-component integrable couplings system 总被引:3,自引:0,他引:3 下载免费PDF全文
A new simple loop algebra GM is constructed, which is devoted to the establishing of an isospectral problem. By making use of the Tu scheme, the multi-component Tu hierarchy is obtained.Furthermore, an expanding loop algebra FM of the loop algebra GM is presented. Based on the FM, the multi-component integrable coupling system of the multi-component Tu hierarchy has been worked out. The method can be applied to other nonlinear evolution equation hierarchies. 相似文献
16.
References: 《理论物理通讯》2007,47(1):19-21
Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out. 相似文献
17.
The trace identity is extended to the general loop algebra. The
Hamiltonian structures of the integrable systems concerning vector
spectral problems and the multi-component integrable hierarchy can be
worked out by using the extended trace identity. As its
application, we have obtained the Hamiltonian structures of the Yang
hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell
(M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy
separately. 相似文献
18.
In the paper,we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly.By the approach the various loop algebras of the Lie algebra A_1are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained,respectively.A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy.Finally,via two different enlarging Lie algebras of the Lie algebra A_1,we derive two resulting differential-difference integrable couplings of the Toda hierarchy,of course,they are all various discrete expanding integrable models of the Toda hierarchy.When the introduced spectral matrices are higher degrees,the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. 相似文献
19.
Multi-component Harry--Dym hierarchy and its integrable couplings as well as their Hamiltonian structures 总被引:1,自引:0,他引:1 下载免费PDF全文
This paper obtains the multi-component
Harry--Dym (H--D) hierarchy and its integrable couplings by
using two kinds of vector loop algebras \widetilde{G}3 and \widetilde{G}6.
The Hamiltonian structures of the above system are
given by the quadratic-form identity. The method can be used
to produce the Hamiltonian structures of the other
integrable couplings or multi-component hierarchies. 相似文献
20.
A new multi-component integrable coupling system for AKNS equation hierarchy with sixteen-potential functions 下载免费PDF全文
It is shown in this paper that the upper triangular strip matrix of
Lie algebra can be used to construct a new integrable coupling
system of soliton equation hierarchy. A direct application to the
Ablowitz--Kaup--Newell-- Segur(AKNS) spectral problem leads to a
novel multi-component soliton equation hierarchy of an integrable
coupling system with sixteen-potential functions. It is indicated
that the study of integrable couplings when using the upper triangular
strip matrix of Lie algebra is an efficient and straightforward
method. 相似文献