标题： 关于微分序列 显示英文标题

标题： On Differential Sequences

摘要： 我们引入了常微分方程的微分序列的概念。 这是由基于演化偏微分方程的相关研究所激发的。 我们从对称性分析、奇异性分析以及识别序列中每个成员的完整对称群的角度来讨论Riccati序列。 奇异性分析揭示了领先项系数和不同主分支的共振值的重要结构。 对于通过递归性质定义而非显式形式给出的微分方程，进行了对称性性质的完整证明。 显示英文摘要

摘要： We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis, singularity analysis and identification of the complete symmetry group for each member of the Sequence. The singularity analysis reveals considerable structure for the values of the coefficients of the leading-order terms and resonances of the different principal branches. Full proofs of the symmetry properties are performed for differential equations defined by their recursion properties and not given in explicit form.