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1.
XU Xi-Xiang YANG Hong-Xiang LU Rong-Wu 《理论物理通讯》2008,50(12):1269-1275
A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems. 相似文献
2.
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
3.
Based on semi-direct sums of Lie subalgebra \tilde{G}, a higher-dimensional 6 x 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derivedfrom a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity --- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we provethat the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems. 相似文献
4.
Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems. 相似文献
5.
A type of higher-dimensional loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity. 相似文献
6.
7.
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
8.
Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated. 相似文献
9.
Staring from a discrete matrix
spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess
non-local Lax pairs. The Hamiltonian structures are established for the
resulting hierarchy by the discrete trace identity. Liouville integrability
of resulting hierarchy is demonstrated. 相似文献
10.
A discrete matrix spectral problem and the associated hierarchy of
Lax integrable lattice equations are presented, and it is shown that
the resulting Lax integrable lattice equations are all
Liouville integrable discrete Hamiltonian systems. A new integrable
symplectic map is given by binary Bargmann constraint of the resulting
hierarchy. Finally, an infinite set of conservation laws is given
for the resulting hierarchy. 相似文献
11.
Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out. 相似文献
12.
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
13.
Starting from a discrete spectral problem, a hierarchy of integrable lattice soliton equations is derived. It is shown that the hierarchy is completely integrable in the Liouville sense and possesses discrete bi-Hamiltonian structure. A new integrable
symplectic map and finite-dimensional integrable systems are given
by nonlinearization method. The binary Bargmann constraint gives
rise to a Bäcklund transformation for the resulting
integrable lattice equations. At last, conservation laws of the
hierarchy are presented. 相似文献
14.
By considering (2+1)-dimensional non-isospectral discrete zero curvature equation, the (2+1)-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the (2+1)- dimensional Toda lattice hierarchy are given. Finally, the (2+1)-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem. 相似文献
15.
Two different integrable couplings of the modified Tu hierarchy are obtained under the zero curvature equation by using two higher dimension Lie algebras. Furthermore, a complex Hamiltonian structures of the second integrable couplings is presented by taking use of the variational identity. 相似文献
16.
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
17.
YU Fa-Jun ZHANG Hong-Qing 《理论物理通讯》2008,50(9):561-564
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally. 相似文献
18.
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
19.
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of
soliton equation hierarchy in this paper. A direct application to
the fractional cubic Volterra lattice spectral problem leads to a
novel integrable coupling system of soliton equation hierarchy. It
is also indicated that the study of discrete integrable couplings
by using the Kronecker product is an efficient and straightforward method. This method can be used generally. 相似文献
20.
A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related tothis spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are givenby nonlinearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resultingintegrable lattice equations. 相似文献