非完整D-模的Newton-Puixix级数及其因式分解
Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring
摘要：
本文引入分数阶导数级数的概念，证明了任意两个自变量的线性偏微分方程都有系数来自零特征微分闭域的分数阶导数级数解.将所得结果从单个方程推广到具有无穷维解空间的$D$ -模（即. e.非完整$D$ -模块）。作为应用程序，我们设计的算法处理一阶因子的线性部分微分算子，特别是寻找所有（右或左）的一阶因子。
英文摘要：
We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field of zero characteristic. The obtained results are extended from a single equation to $D$-modules having infinite-dimensional space of solutions (i. e. non-holonomic $D$-modules). As applications we design algorithms for treating first-order factors of a linear partial differential operator, in particular for finding all (right or left) first-order factors.
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