Differential Galois integrability obstructions for nonlinear three-dimensional differential systems.
Differential Galois integrability obstructions for nonlinear three-dimensional differential systems.
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DOI：
10.1063/1.5128587
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发表时间：
2020-01
期刊：
影响因子：
2.9
通讯作者：
W. Szumiński;M. Przybylska
中科院分区：
文献类型：
--
作者：
W. Szumiński;M. Przybylska
在这篇简短的通讯中，我们处理了非线性三维微分系统的可积性分析。这些系统的右边是线性的一个变量，这使得人们能够找到明确的一个特定的解决方案，并计算变分方程沿着这个解决方案。通过分析微分Galois变分方程群的性质，得到了两个函数独立的有理第一积分完全可积、B-可积和部分可积的条件.它们具有非常简单的数字形式，这对于检查它们是否是适当的整数是必要的。所得到的条件的应用程序的一些示例性的非线性三维微分系统。
In this short communication, we deal with an integrability analysis of nonlinear three-dimensional differential systems. Right-hand sides of these systems are linear in one variable, which enables one to find explicitly a particular solution and to calculate variational equations along this solution. The conditions for the complete integrability with two functionally independent rational first integrals for B-integrability and the partial integrability are obtained from an analysis of properties of the differential Galois group of variational equations. They have a very simple form of numbers, which is necessary to check whether they are appropriate integers. An application of the obtained conditions to some exemplary nonlinear three-dimensional differential systems is shown.