共查询到20条相似文献,搜索用时 695 毫秒
1.
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
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
2.
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
3.
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
4.
The multicomponent (2+1)-dimensional Glachette-Johnson (GJ) equation hierarchy and its super-integrable coupling system
下载免费PDF全文
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent (2+1)-dimensional Glachette-Johnson (G J) hierarchy is given. Finally, the super-integrable coupling system of multicomponent (2+1)-dimensional GJ hierarchy is established through enlarging the spectral problem. 相似文献
5.
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
6.
An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov-Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered. 相似文献
7.
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
8.
We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra \bar{E} of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson (GJ) hierarchy whose Hamiltonian structure can
also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra \tilde{E} of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell (KN) hierarchy which, consisting of two arbitrary parametersα andβ, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra \tilde{F} of the Lie algebra F to obtain an
expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations. 相似文献
9.
An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented. 相似文献
10.
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
11.
Though various integrable
hierarchies of evolution equations were obtained by choosing
proper U in zero-curvature equation Ut-Vx+[U,V]=0, but in this paper, a new integrable hierarchy possessing
bi-Hamiltonian structure is worked out
by selecting V with spectral potentials.
Then its expanding Lax integrable model of the hierarchy possessing a simple
Hamiltonian operator \widetilde{J} is presented
by constructing a subalgebra
\widetilde{G } of the loop algebra \widetilde A2. As
linear expansions of the above-mentioned integrable hierarchy and
its expanding Lax integrable model with respect to their
dimensional numbers, their (2+1)-dimensional forms are derived
from a (2+1)-dimensional zero-curvature equation. 相似文献
12.
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
13.
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
14.
A new Lie algebra G and its two types of loop algebras \tilde{G1} and \tilde{G2} are constructed. Basing on \tilde{G1} and \tilde{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. 相似文献
15.
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
16.
The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure
下载免费PDF全文
![点击此处可从《中国物理》网站下载免费的PDF全文](/ch/ext_images/free.gif)
In this paper a type of 9-dimensional vector loop algebra \tilde{F}
is constructed, which is devoted to establish an isospectral problem.
It follows that a Liouville integrable coupling system of the m-AKNS
hierarchy is obtained by employing the Tu scheme, whose Hamiltonian
structure is worked out by making use of constructed quadratic
identity. The method given in the paper can be used to obtain many
other integrable couplings and their Hamiltonian structures. 相似文献
17.
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
![点击此处可从《中国物理 B》网站下载免费的PDF全文](/ch/ext_images/free.gif)
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
18.
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
19.
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
20.
A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with \tilde{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 \tilde{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. 相似文献