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1.
In [E.G. Fan, Phys. Lett. A 372 (2008) 6368], Fan present a lattice hierarchy and its continuous limits. In this Letter, we extend this method, by introducing a complex discrete spectral problem, a coupling lattice hierarchy is derived. It is shown that a new sequence of combinations of complex lattice spectral problem converges to the integrable coupling couplings of soliton equation hierarchy, which has the integrable coupling system of AKNS hierarchy as a continuous limit. 相似文献
2.
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
3.
It is shown that the Kronecker product can be applied to construct a new integrable coupling system of discrete soliton equation hierarchy in this Letter. A direct application to the generalized Toda lattice spectral problem leads to a novel integrable coupling system. It is also indicated that the study of integrable couplings by using of the Kronecker product is an efficient and straightforward method. 相似文献
4.
Two hierarchies of nonlinear integrable positive and negative lattice models are derived from a discrete spectral problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws of the positive hierarchy, then, the integrable coupling systems of the positive hierarchy are derived from enlarging Lax pair. 相似文献
5.
Engui Fan 《Physics letters. A》2008,372(42):6368-6374
By introducing a discrete spectral problem, we derive a lattice hierarchy which is integrable in Liouville's sense and possesses a multi-Hamiltonian structure. It is show that the discrete spectral problem converges to the well-known AKNS spectral problem under a certain continuous limit. In particular, we construct a sequence of equations in the lattice hierarchy which approximates the AKNS hierarchy as a continuous limit. 相似文献
6.
Fajun Yu 《Physics letters. A》2008,372(24):4353-4360
In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity. 相似文献
7.
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
8.
《Physics letters. A》2006,349(6):439-445
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula. 相似文献
9.
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
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.
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
12.
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
13.
Xi-Xiang Xu 《Physics letters. A》2010,374(3):401-410
An integrable coupling family of Merola-Ragnisco-Tu lattice systems is derived from a four-by-four matrix spectral problem. The Hamiltonian structure of the resulting integrable coupling family is established by the discrete variational identity. Each lattice system in the resulting integrable coupling family is proved to be integrable discrete Hamiltonian system in Liouville sense. Ultimately, a nonisospectral integrable lattice family associated with the resulting integrable lattice family is constructed through discrete zero curvature representation. 相似文献
14.
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
15.
In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity. 相似文献
16.
Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that thehierarchy possesses a Hamiltonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way. 相似文献
17.
Xi-Xiang Xu 《Physics letters. A》2008,372(20):3683-3693
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems. 相似文献
18.
In this paper, we extend a (2+2)-dimensional continuous zero curvature equation to (2+2)-dimensional discrete zero curvature equation, then a new (2+2)-dimensional cubic Volterra lattice hierarchy is obtained. Fhrthermore, the integrable coupling systems of the (2+2)-dimensional cubic Volterra lattice hierarchy and the generalized Toda lattice soliton equations are presented by using a Lie algebraic system sl(4). 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.
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