Q型ABS方程的奇性
Singularities of Type-Q ABS Equations
摘要：
Q型方程位于Adler，Bobenko和Suris（ABS）在对KdV型可积偏微分方程的离散对应物进行分类时所引入的方程族的顶层。我们问什么奇异性是可能的，在这些方程的解决方案，并检查之间的关系的奇异性和主要的可积性功能的多维一致性。这些问题被认为是在全球范围内设置，因此扩展了以前的考虑奇异性已本地。出现的是一些简单的几何标准，确定允许的奇点，和有趣的发现，一般的奇点的存在导致故障的全球一致性，这样的系统，尽管他们的本地一致性属性。这种失败是全球一致的量化引入一个自然的概念，孤立的奇点单值。
英文摘要：
The type-Q equations lie on the top level of the hierarchy introduced by Adler, Bobenko and Suris (ABS) in their classification of discrete counterparts of KdV-type integrable partial differential equations. We ask what singularities are possible in the solutions of these equations, and examine the relationship between the singularities and the principal integrability feature of multidimensional consistency. These questions are considered in the global setting and therefore extend previous considerations of singularities which have been local. What emerges are some simple geometric criteria that determine the allowed singularities, and the interesting discovery that generically the presence of singularities leads to a breakdown in the global consistency of such systems despite their local consistency property. This failure to be globally consistent is quantified by introducing a natural notion of monodromy for isolated singularities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
