arXiv 2104.030732021-04math.DS

具有齐次二次右端项的两个自治一阶常微分方程组的显式可解系统

Explicitly solvable systems of two autonomous first-order Ordinary Differential Equations with homogeneous quadratic right-hand sides

Francesco Calogero, Farrin Payandeh

备注：: 18 pages
发表信息：: Open Communications in Nonlinear Mathematical Physics, Volume 1 (May 20, 2021) ocnmp:7336
DOI：: 10.46298/ocnmp.7336

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AI总结：

本文识别了具有齐次二次右端项的两个一阶常微分方程组中一个由两个代数约束刻画的显式可解特例，并将其扩展至非齐次情形，包括等时系统。

摘要：

在简要回顾非线性常微分方程组可解性这一性质可能具有的各种含义后，我们识别出具有齐次二次右端项的两个一阶常微分方程组的一个特例，该特例是显式可解的。该特例由对该系统进行刻画的6个先验任意参数上的2个显式代数约束所确定。我们还确定了该模型向非齐次二次右端项情形的简单扩展，包括等时情形。

英文摘要：

After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which is explicitly solvable. It is identified by 2 explicit algebraic constraints on the 6 a priori arbitrary parameters that characterize this system. Simple extensions of this model to cases with nonhomogeneous quadratic right-hand sides are also identified, including isochronous cases.

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