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1.
The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure 下载免费PDF全文
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
2.
A new simple loop algebra is constructed, which is devote to establishing an isospectral problem. By making use of Tu scheme,
NLS-MKdV hierarchy is obtained. Again via expanding the loop algebra above, another higher-dimensional loop algebra is presented.
It follows that an integrable coupling of NLS-MkdV hierarchy is given. Also, the trace identity is extended to the quadratic-form
identity and the Hamiltonian structures of the NLS-MKdV hierarchy and integrable coupling of NLS-MkdV hierarchy are obtained
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
3.
Based on the constructed Lie superalgebra,the super-classical-Boussinesq hierarchy is obtained.Then,its superHamiltonian structure is obtained by making use of super-trace identity.Furthermore,the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville. 相似文献
4.
A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations 下载免费PDF全文
A new eight-dimensional Lie superalgebra is constructed
and two isospectral problems with six potentials are designed.
Corresponding hierarchies of nonlinear evolution equations, as well
as super-AKNS and super-Levi, are derived. Their super-Hamiltonian
structures are established by making use of the supertrace identity,
and they are integrable in the sense of Liouville. 相似文献
5.
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
6.
References: 《理论物理通讯》2007,47(5):773-776
A vector loop algebra and its extended loop algebra are proposed, which are devoted to obtaining the Tu hierarchy. By making use of the extended trace identity, the Harniltonian structure of the Tu hierarchy is constructed. Furthermore, we apply the quadratic-form identity to the integrable coupling system of the Tu hierarchy. 相似文献
7.
XU Xi-Xiang 《理论物理通讯》2012,57(6):953-960
A family of integrable differential-difference equations is derived from a new matrix spectral problem. The Hamiltonian forms of obtained differential-difference equations are constructed. The Liouville integrability for the obtained integrable family is proved. Then, Bargmann symmetry constraint of the obtained integrable family is presented by binary nonliearization method of Lax pairs and adjoint Lax pairs. Under this Bargmann symmetry constraints, an integrable symplectic map and a sequences of completely integrable finite-dimensional Hamiltonian systems in Liouville sense are worked out, and every integrable differential-difference equations in the obtained family is factored by the integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system. 相似文献
8.
<正>A new coupled integrable dispersionless equation is presented by considering a spectral problem.A Darboux transformation for the resulting coupled integrable dispersionless equation is constructed with the help of spectral problems.As an application,the N-soliton solution of the coupled integrable dispersionless equation is explicitly given. 相似文献
9.
The trace identity is extended to the quadratic-form identity. The Hamiltonian
structures of the multi-component Guo hierarchy, integrable coupling of Guo
hierarchy and (2+1)-dimensional Guo hierarchy are obtained 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
10.
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
11.
密度矩阵重正化群方法(DMRG)在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器(CPU)和图形处理器(GPU)的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到104,使用的GPU显存小于12 GB. 相似文献
12.
Kostyantyn Zheltukhin Natalya Zheltukhina 《Journal of Nonlinear Mathematical Physics》2018,25(1):166-177
We consider the discretization of Darboux integrable equations. For each of the integrals of a Laine equation we constructed either a semi-discrete equation which has that integral as an n-integral, or we proved that such an equation does not exist. It is also shown that all constructed semi-discrete equations are Darboux integrable. 相似文献
13.
The trace identity is extended to the general loop algebra. The
Hamiltonian structures of the integrable systems concerning vector
spectral problems and the multi-component integrable hierarchy can be
worked out by using the extended trace identity. As its
application, we have obtained the Hamiltonian structures of the Yang
hierarchy, the Korteweg-de--Vries (KdV) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur (M-AKNS) hierarchy, the
multi-component Ablowitz--Kaup--Newell--Segur Kaup--Newell
(M-AKNS--KN) hierarchy and a new multi-component integrable hierarchy
separately. 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.
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed. 相似文献
16.
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed. 相似文献
17.
YAN Qing-You QI Jian-Xun 《理论物理通讯》2006,46(2):203-208
Two types of Lie algebras are constructed, which are directly used to deduce the two resulting integrable coupling systems with multi-component potential functions. Many other integrable couplings of the known integrable systems may be obtained by the approach. 相似文献
18.
YAN Qing-You QI Jian-Xun 《理论物理通讯》2006,46(8)
Two types of Lie algebras are constructed, which are directly used to deduce the two resulting integrable coupling systems with multi-component potential functions. Many other integrable couplings of the known integrable systems may be obtained by the approach. 相似文献
19.
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
20.
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
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