共查询到18条相似文献,搜索用时 374 毫秒
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对已知的Lie代数An-1作直接推广得到一类新的Lie代数gl(n,C).为应用方便,本文只考虑Lie代数gl(3,C)情形.构造了gl(3,C)的一个子代数,通过对阶数的规定,得到了一类新的loop代数.作为其应用,设计了一个新的等谱问题,得到了一个新的Lax对.利用屠格式获得了一族新的可积系统,具有双Hamilton结构,且是Liouville可积系.作为该方程族的约化情形,得到了新的耦合广义Schrdinger方程.
关键词:
Lie代数
可积系
Hamilton结构 相似文献
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蛋白质分子链的非线性激发的孤子模型的一个改进解 总被引:1,自引:1,他引:0
通过仔细考察蛋白质分子链中体系运动方程的非线性项,得到了一个与通常非线性Schrdinger方程不同的修正的非线性Schrdinger方程,并求得了一个改进孤子解. 相似文献
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利用Landau-Lifshitz 方程,研究了具有非均匀交换各向异性的半无限大铁磁体的非线性表 面自旋波理论。导出了部分钉扎纯交换铁磁介质的磁化强度所满足的边界条件和非线性表面 自旋波的色散关系,并获得了自旋波振幅沿z方向驻波的一维非线性Schrdinger方程和包 络振幅沿平面传播的二维非线性Schrdinger方程,结果表明铁磁体磁化强度的包络振幅随时空变化的性质是由二维非线性Schrdinger方程决定的。因此预言铁磁介质的表面非线性激发应是二维孤波的形式。对于弱非线性表面自旋波,对非线性Schrdinger方程存在孤子形式解的可能性作了讨论.
关键词:
表面自旋波
Landau-Lifshitz方程
非线性Schrdinger方程
孤子 相似文献
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将一维定态Schrdinger方程转化为等价的哈密顿正则方程,并采用辛 格式计算了7Li2分子的振动能级。 相似文献
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量子通信是一个量子密钥分发过程,目前采用的通信技术严重制约了量子密钥分发的比特率.将多输入多输出(MIMO)技术应用于量子通信系统,提高量子密钥分发的比特率,促进量子通信向高速大容量发展.然而,量子场本身不可避免地存在量子噪声约束容量的增长,限制了可利用空间资源,即空间自由度.文中采用光子场的量子化和满足Schrdinger方程条件的电磁场波动方程推导出MIMO量子信道的空间自由度上限,为开发稳健的MIMO量子通信空时处理算法和优化设计高性能MIMO量子通信系统提供理论基础和技术支持.
关键词:
多输入多输出
量子密钥分发
Schrdinger方程
光子场的量子化 相似文献
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An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system
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A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented. 相似文献
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A subalgebra of loop algebra A2^~ and its expanding loop algebra G^- are constructed. It follows that both resulting integrable Hamiltonian hierarchies are obtained. As a reduction case of the first hierarchy, a generalized nonlinear coupled Schroedinger equation, the standard heat-conduction and a formalism of the well known Ablowitz, Kaup, Newell and Segur hierarchy are given, respectively. As a reduction case of the second hierarchy, the nonlinear Schroedinger and modified Korteweg de Vries hierarchy and a new integrable system are presented. Especially, a coupled generalized Burgers equation is generated. 相似文献
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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
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XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 《理论物理通讯》2005,44(12)
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multicomponent integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 相似文献
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Multi-component Dirac equation hierarchy and its multi-component integrable couplings system 总被引:2,自引:0,他引:2
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A general scheme for generating a multi-component
integrable equation hierarchy is proposed. A simple
3M-dimensional loop algebra \tilde{X} is produced. By taking
advantage of \tilde{X}, a new isospectral problem is established
and then by making use of the Tu scheme the multi-component Dirac
equation hierarchy is obtained. Finally, an expanding loop algebra
\tilde{F}M of the loop algebra \tilde{X} is presented. Based
on the \tilde{F}M, the multi-component integrable coupling
system of the multi-component Dirac equation hierarchy is
investigated. The method in this paper can be applied to other
nonlinear evolution equation hierarchies. 相似文献
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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
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XIA Tie-Cheng YOU Fu-Cai 《理论物理通讯》2005,44(11)
A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach. 相似文献
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XIA Tie-Cheng YOU Fu-Cai ZHAO Wen-Ying 《理论物理通讯》2005,44(6):990-996
A simple 3M-dimensional loop algebra X is produced, whose commutation operation defined by us is A1 as simple and straightforward as that in the loop algebra A1. It follows that a general scheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then by making use of the Tu scheme the well-known multi-component Levi hierarchy is obtained. Finally, an expanding loop algebra FM of the loop algebra .X is presented, based on the FM, the multi-component integrable coupling system of the multi-component Levi hierarchy is worked out. The method in this paper can be applied to other nonlinear evolution equation hierarchies. 相似文献