【中文摘要】本文研究了与离散3×3矩阵谱问题相联系的Belov-Chaltikian lattice方程族的Hamilton结构及其无穷守恒律。文中首先从3×3矩阵谱问题问题(0.2)出发,借助离散零曲率方程导出与这个谱问题相联系的一族非线性微分差分方程,其中第一个非平凡的方程即为Belov-Chaltikian lattice方程；然后利用迹恒等式构造该方程的Hamilton结构；最后给出了方程的无穷守恒律,并在m=1的情况下证明了守恒律。
【英文摘要】In this paper, we study the Hamiltonian structures and infinitely many conservation laws of Belov-Chaltikian lattice equation, which related to the discrete 3×3 matrix spec-tral problem. Starting with the matrix spectral problem (0.2), a hierarchy of nonlinear differential-difference equations which contains
Belov-Chalkian as its first unform equation is proposed, with the help of the discrete zero-curvature equation. Then the Hamiltonian structures for the hierarchy are derived from the trace identity. At last, the infinitely many conservation laws of the hierarchy are obtained and the correctness was proved
while m=1.
【关键词】离散谱问题 微分差分方程 Hamilton结构 无穷守恒律
【英文关键词】Discrete spectral problem
differential-difference equation Hamilton struc-tures infinitely many conservation laws
【目录】一族非线性微分差分方程的哈密顿结构及其守恒律摘要4-5
Abstract5
§0 引言7-12
§1 Belov-Chaltikian
§3
lattice方程族12-17无穷多守恒律23-27
§2 方程族的Hamilton结构17-23参考文献27-31
致谢31
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