共查询到18条相似文献,搜索用时 46 毫秒
1.
该文利用一个非线性方程是Hamiltion方程的充要条件,给出将相应KP方程的线性问题约束为1+1维Hamilton方程时,位势对称约束的完全形式. 相似文献
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马文秀 《数学物理学报(A辑)》1994,(4)
该文对具有Lenard递推结构的发展方程族,通过转换速推结构为一个算子方程给出了Lax表示的一种理论描述.这种描述可应用于各种1+1维可积系统族Lax表示的寻求之中,本文仅就KdV可积族和Antonowicz—Fordy可积族详细阐述了Lax表示的具体构造过程. 相似文献
4.
Lax表示的变形与Hamilton方程族的Lax表示 总被引:1,自引:0,他引:1
本文首先给出了构造演化方程族的Lax表示的马文秀方法的一种变形,后对这一方法作了改进,使之适用于Hamilton形式的方程族.作为应用,得到了具有非等谱Lax表示的杨方程族. 相似文献
5.
孤子族的生成及换位表示的一般结构 总被引:2,自引:0,他引:2
本文通过对谱问题ψx=U(u,λ)ψ的直接研究,利用谱梯度提供一条获得孤子方程族的途径,进一步,我们给出了孤子方程换位表示的一般结构,同时我们还将看到同一个谱问题可产生两族不同的孤子发展方程。 相似文献
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微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算. 相似文献
7.
贾屹峰 《数学的实践与认识》2019,(9)
基于微分特征列法和微分带余除法,给出了利用拟微分算子构造非线性发展方程1+1维和2+1维Lax表示的新算法.新算法减少了运算步骤,简化了计算过程,是微分特征列法在可积系统领域一个新的应用. 相似文献
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D—AKNS族的换位表示 总被引:4,自引:0,他引:4
本文根据曹策问教授的想法,求得了与D-AKNS族发展方程相联系的特征值之泛函梯度与Lenard算子对;并由此得到了D-AKNS族非线性发展方程的换位表示。文末还讨论了换位表示与定态D-AKNS方程之间的关系. 相似文献
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令H~∞(D)表示单位圆盘D上的有界解析函数全体构成的代数,对于■∈H~∞(D),在某种条件下,证明T=M■是一个指标为n的Cowen-Douglaus算子,并且给出了■(T)/rad■(T)可交换的一个充分条件.当n=1时,刻画了T的换位. 相似文献
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In this paper, the authors define the noncommutative constrained
Kadomtsev-Petviashvili (KP) hierarchy and multi-component
noncommutative constrained KP hierarchy. Then they give the
recursion operators for the noncommutative constrained KP (NcKP)
hierarchy and multi-component noncommutative constrained KP (NmcKP)
hierarchy. The authors hope these studies might be useful in the
study of D-brane dynamics whose noncommutative coordinates emerge
from limits of the M theory and string theory. 相似文献
12.
M. Kazarian 《Advances in Mathematics》2009,221(1):1-21
Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge integrals like Witten's conjecture, Virasoro constrains, Faber's λg-conjecture, etc. Among other results we show that a properly arranged generating function for Hodge integrals satisfies the equations of the KP hierarchy. 相似文献
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首先讨论了约束离散KP可积方程族一种等价形式:差分算子的商.接下来,利用这种新的描述形式,构造了约束离散KP方程族的完全Virasoro对称. 相似文献
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The discrete Ablowitz-Ladik hierarchy with four potentials and the Hamiltonian structures are derived. Under a constraint between the potentials and eigenfunctions, the nonlinearization of the Lax pairs associated with the discrete Ablowitz-Ladik hierarchy leads to a new symplectic map and a class of finite-dimensional Hamiltonian systems. The generating function of the integrals of motion is presented, by which the symplectic map and these finite-dimensional Hamiltonian systems are further proved to be completely integrable in the Liouville sense. Each member in the discrete Ablowitz-Ladik hierarchy is decomposed into a Hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map. 相似文献
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With the aid of Mullin-Rota's substitution rule, we show that the Sheffertype differential operators together with the delta operators ? and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical fomulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of(∞~m) degree formulas for m ≥ 3 with m ≡ 1(mod 2) and m ≡ 1(mod3), respectively. 相似文献
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关于Delta算子的广义Taylor公式的余项估计 总被引:1,自引:0,他引:1
本文对哑演算中Rota提出的至今尚未解决的广义Talor公式的余项估计问题进行了研究。获得了Delta算子关于一般函数的一个不同于Lagrange型的结果,并解决了二阶Delta算子的余项估计问题。 相似文献
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讨论了四对谱问题、相应的保谱方程族以及它们Lax表示的等价住,并利用这种等价关系可导出一些方程的Lax表示. 相似文献
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Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each
quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix which automatically satisfies the Yang–Baxter equation. Applying the vector representation π, which acts on the vector module V, to the left-hand side of a universal R-matrix gives a Lax operator. In this article a Lax operator is constructed for the quantised orthosymplectic superalgebras
U
q
[osp(m|n)] for all m > 2, n ≥ 0 where n is even. This can then be used to find a solution to the Yang–Baxter equation acting on V ⊗ V ⊗ W, where W is an arbitrary U
q
[osp(m|n)] module. The case W = V is studied as an example.
Presented by A. Verschoren. 相似文献