共查询到20条相似文献,搜索用时 93 毫秒
1.
YU Fa-Jun ZHANG Hong-Qing 《理论物理通讯》2007,47(3):393-396
The upper triangular matrix of Lie algebra is used to construct integrable couplings of discrete solition equations. Correspondingly, a feasible way to construct integrable couplings is presented. A nonlinear lattice soliton equation spectral problem is obtained and leads to a novel hierarchy of the nonlinear lattice equation hierarchy. It indicates that the study of integrable couplings using upper triangular matrix of Lie algebra is an important step towards constructing integrable systems. 相似文献
2.
R. Aldrovandi V. C. de Andrade A. L. Barbosa J. G. Pereira 《International Journal of Theoretical Physics》2003,42(12):2955-2970
Applied to the electroweak interactions, the theory of Lie algebra extensions suggests a mechanism by which the boson masses are generated without resource to spontaneous symmetry breaking. It starts from a gauge theory without any additional scalar field. All the couplings predicted by the Weinberg–Salam theory are present, and a few others which are nevertheless consistent within the model. 相似文献
3.
A new higher-dimensional Lie algebra is constructed, which
is used to generate multiple integrable couplings simultaneously. From
this, we come to a general approach for seeking multi-integrable
couplings of the known integrable soliton equations. 相似文献
4.
William P. Joyce 《Czechoslovak Journal of Physics》2004,54(11):1335-1339
We present a generalization of graded Lie algebra as an algebraic version of recoupling theory. In order to construct a universal envelope we generalise the usual notion of algebra to that of -algebra. We state the basis of the envelope. 相似文献
5.
By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92],
three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are
higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and
quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations. 相似文献
6.
A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics. 相似文献
7.
A 3? 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3? 3 Lie subalgebra into a 2? 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. 相似文献
8.
ZHANG Yu-Feng DONG Huang-He Honwah Tam 《理论物理通讯》2007,48(2):215-226
Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given. 相似文献
9.
Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra A1 are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given. 相似文献
10.
With the help of a known Lie algebra,two new high order Lie algebras are constructed.It is remarkable that they have different constructing approaches.The first Lie algebra is constructed by the definition of integrable couplings.the second one by an extension of Lie algebra,Then by making use of Tu scheme,a generalized AKNS hierarchy and another new hierarchy are obtained.As a reduction case of the first hierarchy,a kind of coupled KdV equation is presented.As a reduction case of the second one,a new coupled Schroedinger equation is given. 相似文献
11.
A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is
presented. Finally, the integrable couplings of the obtained system
is worked out by the expanding matrix Loop algebra. 相似文献
12.
George W. Bluman Omar Mrani-Zentar Deshin Finlay 《Journal of Nonlinear Mathematical Physics》2018,25(4):528-557
It is shown explicitly how one can obtain elements of Lie groups as compositions of products of other elements based on the commutator properties of associated Lie algebras. Problems of this kind can arise naturally in control theory. Suppose an apparatus has mechanisms for moving in a limited number of ways with other movements generated by compositions of allowed motions. Two concrete examples are: (1) the restricted parallel parking problem where the commutator of translations in y and rotations in the xy-plane yields translations in x. Here the control problem involves a vehicle that can only perform a series of translations in y and rotations with the aim of efficiently obtaining a pure translation in x; (2) involves an apparatus that can only perform rotations about two axes with the aim of performing rotations about a third axis. Both examples involve three-dimensional Lie algebras. In particular, the composition problem is solved for the nine three- and four-dimensional Lie algebras with non-trivial solutions. Three different solution methods are presented. Two of these methods depend on operator and matrix representations of a Lie algebra. The other method is a differential equation method that depends solely on the commutator properties of a Lie algebra. Remarkably, for these distinguished Lie algebras the solutions involve arbitrary functions and can be expressed in terms of elementary functions. 相似文献
13.
A Maple Package to Compute Lie Symmetry Groups and Symmetry Reductions of (1+1)-Dimensional Nonlinear Systems 下载免费PDF全文
Armed with the computer algebra system Maple, using a direct algebraic substitution method, we obtain Lie point symmetries, Lie symmetry groups and the corresponding symmetry reductions of one component nonlinear integrable and nonintegrable equations only by clicking the ‘Enter' key. Abundant (1+1)-dimensional nonlinear mathematical physical systems are analysed effectively by using a Maple package LieSYMGRP proposed by us. 相似文献
14.
A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie algebra Be, respectively. 相似文献
15.
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
16.
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
17.
Li Li 《Physics letters. A》2009,373(39):3501-3506
In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit. 相似文献
18.
ZHANG Yu-Feng LIU Jing 《理论物理通讯》2008,50(8):289-294
By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92], three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations. 相似文献
19.
We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory.
This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal
algebra cohomology complex, and endow it with a structure of a
\mathfrakg{\mathfrak{g}}-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric
poly-differential operators. 相似文献
20.
ZHANG Yu-Feng 《理论物理通讯》2008,50(5):1021-1026
A new Lie algebra G of the Lie algebra sl(2) is constructed
with complex entries whose structure constants are real and
imaginary numbers. A loop algebra
˜G
corresponding to the Lie algebra G is constructed, for which it is devoted to
generating a soliton hierarchy of evolution equations under the
framework of generalized zero curvature equation which is derived
from the compatibility of the isospectral problems expressed by
Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and
G2. Using the G2 and its one type of loop algebra
˜G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its
bi-Hamiltonian structure by employing the quadratic-form identity. 相似文献