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利用一个广义等谱问题的相容性得到了一个广义零曲率方程.作为其应用,首先利用loop代数设计了两个广义等谱问题,然后利用零曲率方程导出了两类(2+1)维Lax可积系统. 相似文献
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本文基于loop代数A1的一个子代数,构造了一个新的loop代数G;通过作一个适宜的Lax对变换,成功地将G应用于Levi等谱问题上,求得了Levi谱系的可积耦合,这种方法可以普遍地应用。 相似文献
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基于李超代数,构造了超广义Burgers方程族的非线性可积耦合,并且利用超级恒等式得到了它的超Hamilton结构.此外,该文计算出超广义Burgers方程族的非线性可积耦合的Bargmann对称约束. 相似文献
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可积的与Hamilton形式的NLS-MKdV方程族 总被引:16,自引:1,他引:16
本文基于loop代数A2的一个特殊子代数,设计了一个等谱问题,应用屠规彰格式计算出一族具有Hamilton结构的可积系.此族含有非线性Schrdinger方程与修正的KdV方程,称之为NLS MKdV方程族 相似文献
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Starting from a Tu Guizhang‘s isospectral‘problem, a Lax pair is obtained by means of Tu scheme ( we call it Tu Lax pair ). By applying a gauge transformation between matrices, the Tu Lax pair is changed to its equivalent Lax pair with the traces of spectral matrices being zero, whose compatibility gives rise to a type of Tu hierarchy of equations. By making use of a high order loop algebra constructed by us, an integrable coupling system of the Tu hierarchy of equations are presented. Especially, as reduction cases, the integrable couplings of the celebrated AKNS hierarchy, TD hierarchy and Levi hierarchy are given at the same time. 相似文献
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本文讨论了有扭的仿射李代数 A_2~((2))的一类不在范畴 O 的可积模.证明了这样的模是完全可约的,并且决定了所有的这类不可约模.从而这类模的结构是完全清楚的. 相似文献
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Huanhe Dong 《高等学校计算数学学报(英文版)》2007,16(2):147-154
Under the frame of the (2 1)-dimensional zero curvature equation and Tu model, the (2 1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2 1)-dimensional multi-component integrable system will be investigated. 相似文献
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A set of new matrix Lie algebra is constructed, which is devoted to obtaining a new loop algebra A 2M . Then we use the idea of enlarging spectral problems to make an enlarged spectral problems. It follows that the multi-component AKNS hierarchy is presented. Further, two classes of integrable coupling of the AKNS hierarchy are obtained by enlarging spectral problems. 相似文献
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Based on fractional isospectral problems and general bilinear forms, the generalized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
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Firstly,a vector loop algebra (~G)3 is constructed,by use of it multi-component KN hierarchy is obtained.Further,by taking advantage of the extending vector loop algebras (~G)6 and (~G)9 of (~G)3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively.Finally,Hamiltonian structures of obtained system are given by quadratic-form identity. 相似文献
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利用李群$M_nC$的一个子群我们引入一个线性非等谱问题,该问题的相容性条件可导出演化方程的一个非等谱可积族,该可积族可约化成一个广义非等谱可积族.这个广义非等谱可积族可进一步约化成在物理学中具有重要应用的标准非线性薛定谔方程和KdV方程.基于此,我们讨论在广义非等谱可积族等谱条件下的一个广义AKNS族$u_t=K_m(u)$的$K$对称和$\tau$对称.此外,我们还考虑非等谱AKNS族$u_t=\tau_{N+1}^l$的$K$对称和$\tau$对称.最后,我们得到这两个可积族的对称李代数,并给出这些对称和李代数的一些应用,即生成了一些变换李群和约化方程的无穷小算子. 相似文献