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1.
We propose a systematic approach for generating Hamiltonian tri-integrable couplings of soliton hierarchies. The resulting approach is based on semi-direct sums of matrix Lie algebras consisting of 4 × 4 block matrix Lie algebras. We apply the approach to the AKNS soliton hierarchy, and Hamiltonian structures of the obtained tri-integrable couplings are constructed by the variational identity. 相似文献
2.
Discrete integrable couplings associated with modified Korteweg——de Vries lattice and two hierarchies of discrete soliton equations 下载免费PDF全文
A direct way to construct integrable couplings for discrete systems
is presented by use of two semi-direct sum Lie algebras. As their
applications, the discrete integrable couplings associated with
modified Korteweg--de Vries (m-KdV) lattice and two hierarchies of
discrete soliton equations are developed. It is also indicated that
the study of integrable couplings using semi-direct sums of Lie
algebras is an important step towards the complete classification of
integrable couplings. 相似文献
3.
With non-semisimple Lie algebras, the trace identity was generalized to discrete spectral problems. Then the corresponding
discrete variational identity was used to a class of semi-direct sums of Lie algebras in a lattice hierarchy case and obtained
Hamiltonian structures for the associated integrable couplings of the lattice hierarchy. It is a powerful tool for exploring
Hamiltonian structures of discrete soliton equations. 相似文献
4.
By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville sense and possessing
bi-Hamiltonian structure. Two types of semi-direct sums of Lie algebras are proposed, by using of which a practicable way to construct discrete integrable couplings is introduced. As
applications, two kinds of discrete integrable couplings of the
resulting system are worked out. 相似文献
5.
Fajun Yu 《Physics letters. A》2011,375(13):1504-1509
Some integrable coupling systems of existing papers are linear integrable couplings. In the Letter, beginning with Lax pairs from special non-semisimple matrix Lie algebras, we establish a scheme for constructing real nonlinear integrable couplings of continuous soliton hierarchy. A direct application to the AKNS spectral problem leads to a novel nonlinear integrable couplings, then we consider the Hamiltonian structures of nonlinear integrable couplings of AKNS hierarchy with the component-trace identity. 相似文献
6.
This paper derives new discrete integrable system based on discrete
isospectral problem. It shows that the hierarchy is completely
integrable in the Liouville sense and possesses bi-Hamiltonian
structure. Finally, integrable couplings of the obtained system is
given by means of semi-direct sums of Lie algebras. 相似文献
7.
Starting from a spectrai problem, a corresponding soliton hierarchy is proposed, and we construct an integrable coupling system with five dependent variables for the hierarchy by using a class of semi-direct sums of Lie algebras. Moreover, it is shown that the coupling system possesses quasi-Hamiltionian structures, and that infinitely many conserved quantities are obtained. 相似文献
8.
We propose a class
of non-semisimple
matrix loop algebras consisting of
3×3 block matrices,
and form zero curvature equations from the
presented loop algebras to generate bi-integrable couplings.
Applications are made for the AKNS soliton hierarchy and
Hamiltonian structures of the resulting integrable couplings
are constructed by using the associated variational
identities. 相似文献
9.
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
10.
Matrix Lie Algebras and Integrable Couplings 总被引:2,自引:0,他引:2
ZHANG Yu-Feng GUO Fu-Kui 《理论物理通讯》2006,46(5):812-818
Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively. 相似文献
11.
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
12.
A hierarchy of non-isospectral multi-component AKNS equations is derived from an arbitrary order matrix spectral problem. As a reduction, non-isospectral multi-component Schrödinger equations are obtained. Moreover, new non-isospectral integrable couplings of the resulting AKNS soliton hierarchy are constructed by enlarging the associated matrix spectral problem. 相似文献
13.
ZHANG Yu-Feng GUO Fu-Kui 《理论物理通讯》2006,46(11)
Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively. 相似文献
14.
ZHANG Yu-Feng 《理论物理通讯》2011,56(5):805-812
Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti-Johnson (GJ) hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their Hamiltonian structures are also generated. The approach presented in the paper can also
provide nonlinear integrable couplings of other soliton hierarchies of evolution equations. 相似文献
15.
《Physics letters. A》2006,357(6):454-461
With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations. 相似文献
16.
Two kinds of higher-dimensional Lie algebras and their loop algebras are introduced, for which a few expanding integrable models including the coupling integrable couplings of the Broer-Kaup (BK) hierarchy and the dispersive long wave (DLW) hierarchy as well as the TB hierarchy are obtained. From the reductions of the coupling integrable couplings, the corresponding coupled integrable couplings of the BK equation, the DLW equation, and the TB equation are obtained, respectively. Especially, thecoupling integrable coupling of the TB equation reduces to a few integrable couplings of the well-known mKdV equation. The Hamiltonian structures of the coupling integrable couplings of the three kinds of soliton hierarchies are worked out, respectively, by employing the variational identity. Finally, we decompose the BK hierarchy of evolution equations into x-constrained flows and tn-constrained flows whose adjoint representations and the Lax pairs are given. 相似文献
17.
By considering a discrete iso-spectral problem, a hierarchy of bi-Hamiltonian relativistic Toda type lattice equations are revisited. After introducing a semi-direct sum Lie algebras of four by four matrices, integrable coupling system associated with the relativistic Toda type lattice are derived. It is shown that the resulting lattice soliton hierarchy possesses Hamiltonian structures and infinitely many common commuting symmetries as well infinitely many conserved functions. The Liouville integrability of the resulting system is then demonstrated. 相似文献
18.
Liouville integrable discrete integrable system is derived based on discrete isospectral problem. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses bi-Hamiltonian structure. Finally, integrablecouplings of the obtained system is given by means of semi-direct sums of Lie algebras. 相似文献
19.
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
20.
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