论文标题
哈密顿系统，Toda晶格，孤子，lax对加权Z级图
Hamiltonian systems, Toda lattices, Solitons, Lax Pairs on weighted Z-graded graphs
论文作者
论文摘要
我们考虑离散的一维非线性方程，并提出将它们提升为Z级图的过程。我们确定可以将一个维解决方案提升到图上的解决方案的条件。特别是，我们证明了分层图上的静态电势}的存在。我们还表明，即使对于拓扑有趣的图的简单示例，相应的非平凡的松弛对和相关的单一转换也不会提起Z级图上的Lax对。
We consider discrete one dimensional nonlinear equations and present the procedure of lifting them to Z-graded graphs. We identify conditions which allow one to lift one dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons {for static potentials} on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z-graded graph.
