共查询到19条相似文献,搜索用时 171 毫秒
1.
研究线性连续广义系统的Hamilton矩阵及H\-2代数Riccati方程. 提出一个标准的广义H\-2代数Riccati方程及对应的Hamilton矩阵,给出该Hamilton矩阵的几个重要性质. 在此基础上,得到该广义H\-2代数Riccati方程的稳定化解存在的一个充分条件并给出求解方法.此条件具有一般性, 主要定理是正常系统相应结果的推广. 相似文献
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本文基于新的非半单矩阵Lie代数,介绍了构造孤子族非线性双可积耦合的方法,由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构.作为应用,给出Kaup-Newell族的非线性双可积耦合及其Hamilton结构.最后利用源生成理论建立新的公式,并导出带自相容源Kaup-Newell族的非线性双可积耦合方程. 相似文献
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基于新的非半单矩阵李代数,介绍了构造孤子族非线性双可积耦合的方法,由相应的变分恒等式给出了孤子族非线性双可积耦合的Hamilton结构.作为应用,给出了Broer-Kaup-Kupershmidt族的非线性双可积耦合及其Hamilton结构.最后指出了文献中的一些错误,利用源生成理论建立了新的公式,并导出了带自相容源Broer-Kaup-Kupershmidt族的非线性双可积耦合方程. 相似文献
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张玉峰 《数学物理学报(A辑)》2005,25(1):1-10
构造了Loop代数~A_{-1}的一个子代数,利用屠格式导出了一族新的可积孤子方程族,并且是Liouville可积系,具有双Hamilton结构。 相似文献
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本文利用二项式残数表示方法生成(2+1)-维超可积系统. 由这些系统得到了一个新的(2+1)-维超孤子族,它能约化为(2+1)-维超非线性Schrodinger方程. 特别地,我们得到两个具有重要物理应用的结果,一个是(2+1)-维超可积耦合方程,另一个是(2+1)-维的扩散方程. 最后借助超迹恒等式给出了新(2+1)-维超可积系统的Hamilton结构. 相似文献
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《数学物理学报(A辑)》2020,(1)
该文利用Lie超代数B(0,1)导出一个新的广义超孤子族,借助超迹恒等式将广义超孤子族写成超双-Hamilton结构形式.其次,建立了广义超孤子族的自相容源.最后,给出了广义超孤子族的无穷守恒律. 相似文献
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用投影方法求耗散广义Hamilton约束系统的李群积分 总被引:1,自引:0,他引:1
针对耗散广义Hamilton约束系统.通过引入拉格朗日乘子和采用投影技术,给出了一种保持动力系统内在结构和约束不变性的李群积分法.首先将带约束条件的耗散Hamilton系统化为无约束广义Hamilton系统.进而讨论了无约束广义Hamilton系统的李群积分法,最后给出了广义Hamilton约束系统李群积分的投影方法.采用投影技术保证了约束的不变性,引入拉格朗日乘子后,在向约束流形投影时不会破坏原动力系统的李群结构.讨论的内容仅限于完整约束系统,通过数值例题说明了方法的有效性. 相似文献
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《数学物理学报(A辑)》2016,(2)
该文从新谱问题出发,得到一个新的(2+1)-维广义Broer-Kaup-Kupershmidt孤子方程在Lax对非线性化下被分解成可积的常微分方程.接着,给出了一个有限维Hamilton系统并且证明在Liouville意义下是完全可积的.通过引进Abel-Jacobi坐标把Hamilton流进行了拉直,借助Riemannθ函数得到了(2+1)-维Broer-Kaup-Kupershmidt孤子方程的拟周期解. 相似文献
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Yaning Tang Wen-Xiu MaLiang Gao 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):585-592
We presented an integrable coupling hierarchy of a matrix spectral problem with arbitrary order zero matrix r by using semi-direct sums of matrix Lie algebra. The Hamiltonian structure of the resulting integrable couplings hierarchy is established by means of the component trace identities. As an example, when r is 2 × 2 zero matrix specially, the integrable coupling hierarchy and its Hamiltonian structure of the matrix spectral problem are computed. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3454-3461
Two isospectral problems are constructed with the help of a 6-dimensional Lie algebra. By using the Tu scheme, a (1 + 1)-dimensional expanding integrable couplings of the KdV hierarchy is obtained and the corresponding Hamiltonian structure is established. In addition, the 2-order matrix operators proposed by Tuguizhang are extended to the case where some 4-order matrices are given. Based on the extension, a new hierarchy of 2 + 1 dimensions is obtained by the Hamiltonian operator of the above (1 + 1)-dimensional case and the TAH scheme. The new hierarchy of 2 + 1 dimensions can be reduced to a coupled (2 + 1)-dimensional nonlinear equation and furthermore it can be reduced to the (2 + 1)-dimensional KdV equation which has important physics applications. The Hamiltonian structure for the (2 + 1)-dimensional hierarchy is derived with the aid of an extended trace identity. To the best of our knowledge, generating the (2 + 1)-dimensional equation hierarchies by virtue of the TAH scheme has not been studied in detail except to previous little work by Tu et al. 相似文献
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Zdzis?aw Skupień 《Discrete Mathematics》2009,309(22):6382-6390
We construct multigraphs of any large order with as few as only four 2-decompositions into Hamilton cycles or only two 2-decompositions into Hamilton paths. Nevertheless, some of those multigraphs are proved to have exponentially many Hamilton cycles (Hamilton paths). Two families of large simple graphs are constructed. Members in one class have exactly 16 hamiltonian pairs and in another class exactly four traceable pairs. These graphs also have exponentially many Hamilton cycles and Hamilton paths, respectively. The exact numbers of (Hamilton) cycles and paths are expressed in terms of Lucas- or Fibonacci-like numbers which count 2-independent vertex (or edge) subsets on the n-path or n-cycle. A closed formula which counts Hamilton cycles in the square of the n-cycle is found for n≥5. The presented results complement, improve on, or extend the corresponding well-known Thomason’s results. 相似文献
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Zhijun Qiao 《Acta Appl Math》2004,83(3):199-220
This paper provides a new integrable hierarchy. The DP equation: m
t
+um
x
+3mu
x
=0, m=u–u
xx
, proposed recently by Degasperis and Procesi, is the first member in the negative order hierarchy while the first equation in the positive order hierarchy is: m
t
=4(m
–2/3)
x
–5(m
–2/3)
xxx
+(m
–2/3)
xxxxx
. The whole hierarchy is shown Lax-integrable through solving a key matrix equation. To obtain the parametric solutions for the whole hierarchy, we separately discuss the negative order and the positive order hierarchies. For the negative order hierarchy, its 3×3 Lax pairs and corresponding adjoint representations are cast in Liouville-integrable Hamiltonian canonical systems under the Dirac–Poisson bracket defined on a symplectic submanifold of R
6N
. Based on the integrability of those finite-dimensional canonical Hamiltonian systems we give the parametric solutions of all equations in the negative order hierarchy. In particular, we obtain the parametric solution of the DP equation. Moreover, for the positive order hierarchy, we consider a different constraint and process a procedure similar to the negative case to obtain the parametric solutions of the positive order hierarchy. In a special case, we give the parametric solution of the 5th-order PDE m
t
=4(m
–2/3)
x
–5(m
–2/3)
xxx
+(m
–2/3)
xxxxx
. Finally, we discuss the stationary solutions of the 5th-order PDE, which may be included in the parametric solution. 相似文献
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We construct a Lie algebra G by using a semi-direct sum of Lie algebra G1 with Lie algebra G2. A direct application to the TD hierarchy leads to a novel hierarchy of integrable couplings of the TD hierarchy. Furthermore, the generalized variational identity is applied to Lie algebra G to obtain quasi-Hamiltonian structures of the associated integrable couplings. 相似文献
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Jingzhu Wu Xiuzhi Xing Xianguo Geng 《Mathematical Methods in the Applied Sciences》2016,39(14):3925-3931
Based on a general isospectral problem of fractional order, a fractional bilinear form variational identity, the new integrable coupling of fractional L‐hierarchy and the Hamiltonian structures of the integrable coupling of fractional L‐hierarchy are obtained. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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By virtue of zero curvature representations, we are successful to generate the Lax representations of two hierarchies of discrete lattice equations respectively, which are derived from two new and interesting 3 × 3 matrix spectral problems. Moreover, by using the trace identity, the bi-Hamiltonian structures of the above systems are given, and it is shown that they are integrable in the Liouville sense. Finally, infinitely many conservation laws for the second hierarchy of lattice equations are given by a direct method. 相似文献