On generating (2 + 1)-dimensional hierarchies of evolution equations
On generating (2 + 1)-dimensional hierarchies of evolution equations
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DOI：
10.1016/j.cnsns.2014.03.029
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发表时间：
2014-10
期刊：
影响因子：
--
通讯作者：
Yufeng Zhang;Wenjuan Rui
中科院分区：
文献类型：
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作者：
Yufeng Zhang;Wenjuan Rui
利用六维李代数构造了两个等谱问题。利用Tu格式，得到了KdV层次的（1 + 1）维扩展可积耦合，并建立了相应的哈密顿结构。此外，将土归章提出的二阶矩阵算子推广到某些四阶矩阵的情况。在此基础上，利用上述（1 + 1）维情形的哈密顿算子和TAH格式，得到了一个新的2 + 1维层次结构。新的2 + 1维层次可以简化为一个耦合的（2 + 1）维非线性方程，进而可以简化为具有重要物理应用的（2 + 1）维KdV方程。利用扩展的迹恒等式导出了（2 + 1）维层次结构的哈密顿结构。据我们所知，除了Tu等人之前的少量工作外，还没有详细研究过利用TAH方案生成（2 + 1）维方程层次结构。
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.