共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
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
13.
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
14.
With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding(2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation(BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing(2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the(2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the(2+1)-dimensional AKNS equation(also called the Davey-Stewartson hierarchy), a kind of(2+1)-dimensional Schr¨odinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new(2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the(2+1)-dimensional integrable coupling, which is further reduced to the standard(2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known(1+1)-dimensional AKNS hierarchy, the(1+1)-dimensional nonlinear Schr¨odinger equation are all special cases of the(2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the(2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. 相似文献
15.
In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. From the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquist and Estabrook, we study the prolongation structure of the nonlinear integrable couplings of the KdV equation. 相似文献
16.
This Letter reports on a study of the multicomponent discrete integrable equation hierarchy with variable spectral parameters. An instance of new multicomponent lattice equation is obtained. Correspondingly, a feasible way to construct the integrable couplings is presented. It indicates that the study of integrable couplings using the block matrix-form of Lie algebra is an important and effective method. 相似文献
17.
由loop代数的一个子代数出发,构造了一个线性等谱问题,再利用屠格式计算出了一类Liouvelle意义下的可积系统及其双Hamilton结构,作为该可积系统的约化,得到了著名的Schrdinger方程和mKdV方程,因此称该系统为S-mKdV方程族.根据已构造的的子代数,又构造了维数为5的loop代数的一个新的子代数,由此出发设计了一个线性等谱形式,再利用屠格式求得了S-mKdV方程族的一类扩展可积模型.利用这种方法还可以求BPT方程族、TB方程族等谱系的扩展可积模型.因此本方法具有普遍应用价值.最后作为特例,求得了著名的Schrdinger方程和mKdV方程的可积耦合系统. 相似文献
18.
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
19.
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
20.
Nonlinear integrable couplings of a nonlinear Schrdinger-modified Korteweg de Vries hierarchy with self-consistent sources 下载免费PDF全文
By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries(NLS-mKdV) hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated. 相似文献