论文标题
关于可解的谎言代数和普通微分方程的集成方法
On solvable Lie algebras and integration method of ordinary differential equations
论文作者
论文摘要
已经找到了一些更通用的“继承条件”，对于一组给定的对称生成器$ \ {\ Mathbf {Z} _ {\ bar {l}} \} $，在某些耦合的普通微分方程上作用于某些耦合的普通微分方程，一旦将“第一个集成方法”应用于某些Abelian Sub-subgebra Gengerbra of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators of Generators。 $ \ {\ mathbf {z} _ {i} \} $要减少方程系统。我们已经证明了以下定理：可以通过“第一个集成方法”使用某些可解决的子代数的所有生成器，以减少（顺序）和/或（可能）集成方程系统。还提供了必须执行逐步减少过程的特定顺序，并提供仅在四倍方面获得分析解决方案的条件。我们为某些给定最大，可解决的子代数定义了“最佳”概念，并证明了一个定理指出：此代数导致最有利可图的方式，将对称发生器用于手头的集成过程。
Some more general "inheritance conditions" have been found for a given set of symmetry generators $\{\mathbf{Z}_{\bar{l}}\}$ acting on some set of coupled ordinary differential equations, once the "first integration method" has been applied upon some Abelian sub-algebra of generators $\{\mathbf{Z}_{i}\}$ for the system of equations to be reduced. We have proven the following theorem: all the generators of some solvable sub-algebra can be used via the "first integration method" in order to reduce (the order) and/or (possibly) integrate the system of equations. The specific order in which the step by step reduction process has to be performed, and the condition to obtain the analytic solution solely in terms of quadratures, are also provided. We define the notion "optimum" for some given maximal, solvable sub-algebra and prove a theorem stating that: this algebra leads to the most profitable way of using the symmetry generators for the integration procedure at hand.
